{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "WhatIsPython_NOTEBOOK.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3"
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tli2bs6meY8a",
        "colab_type": "text"
      },
      "source": [
        "![alt_text](http://images.tynker.com/blog/wp-content/uploads/DSC_0013-edited-cropped.jpg 'Child using a programming software')\n",
        "\n",
        "# Welcome to the What is Python notebook!\n",
        "#### By the end of this notebook, you will be able to...\n",
        "\n",
        "_1. Understand how to plot linear and quadratic functions in Python._\n",
        "\n",
        "_2. Apply your knowledge of basic coding structures such as variables and operators._\n",
        "\n",
        "_3. Apply your knowledge of linear and quadratic functions and derivatives to understand how the functions written for this notebook work._\n",
        "---\n",
        "\n",
        "Instructions: To run a code block, click on it to __select__ it, and then press __SHIFT__ and __ENTER__. Note that you do __not__ need to understand Python to use this notebook--just run each code cell and observe the plots that follow it.\n",
        "\n",
        "---\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h4c5a0YXeY8i",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# First let's import some libraries...\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "from IPython.display import YouTubeVideo"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iDMZE4JEeY8r",
        "colab_type": "text"
      },
      "source": [
        "While a **TI-89** works fine for plotting these, it can be useful to know how to use Python to customize and plot these functions as well!\n",
        "First, let's walk through how to create and plot a linear function.\n",
        "\n",
        "Before we begin, it may be helpful to refresh yourself linear equations and how to plot them. Run the code below to reveal a **Khan Academy **video on slope-intercept form."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nUqkwZhNeY8s",
        "colab_type": "code",
        "outputId": "812af3ce-28e3-439d-86e0-e315438c61e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        }
      },
      "source": [
        "YouTubeVideo('IL3UCuXrUzE')"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "        <iframe\n",
              "            width=\"400\"\n",
              "            height=\"300\"\n",
              "            src=\"https://www.youtube.com/embed/IL3UCuXrUzE\"\n",
              "            frameborder=\"0\"\n",
              "            allowfullscreen\n",
              "        ></iframe>\n",
              "        "
            ],
            "text/plain": [
              "<IPython.lib.display.YouTubeVideo at 0x7f391b980320>"
            ],
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\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zp6qywF1eY8y",
        "colab_type": "code",
        "outputId": "0e303dfa-721f-4e6e-b545-b0c09f5361c3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "# Now, let's define a function for creating the points of our line\n",
        "def create_line(x,m,b):\n",
        "    y = m * x + b\n",
        "    return y\n",
        "\n",
        "# Now, let's create the line y = 2x + 1\n",
        "x = np.arange(-10,11) # Using the range -10 < x < 10\n",
        "slope = 2\n",
        "y_int = 1\n",
        "y = create_line(x,slope,y_int) # y = 2x + 1\n",
        "\n",
        "# Now, let's plot the line\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Line')\n",
        "plt.show()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j5uwnoQ5eY84",
        "colab_type": "text"
      },
      "source": [
        "Now, let's spice things up a bit--let's add some __points__ to our line."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OjNxkBffeY86",
        "colab_type": "code",
        "outputId": "4a76492f-859d-4c9b-dd94-916c7f249108",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "# Create a point in the range -10 < x < 10\n",
        "x_pt = 0;\n",
        "y_pt = create_line(x_pt,slope,y_int)\n",
        "\n",
        "# Plot the point, along with the original function, on a graph\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.plot(x_pt,y_pt,'r.') # Plot the point as a red dot\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Line')\n",
        "plt.show()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bjhmx5JHeY9C",
        "colab_type": "text"
      },
      "source": [
        "Great! Now, let's look at plotting a __parabola__. First, run the code below to view a Khan Academy video on parabolic functions to refresh your knowledge of them."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nhic4Is2eY9E",
        "colab_type": "code",
        "outputId": "43bde388-6807-40e7-9ab7-de4b39927cd9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 322
        }
      },
      "source": [
        "YouTubeVideo('7QMoNY6FzvM')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "        <iframe\n",
              "            width=\"400\"\n",
              "            height=\"300\"\n",
              "            src=\"https://www.youtube.com/embed/7QMoNY6FzvM\"\n",
              "            frameborder=\"0\"\n",
              "            allowfullscreen\n",
              "        ></iframe>\n",
              "        "
            ],
            "text/plain": [
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DtyC2+/uzbe+6td4Sp9BFLlh0hBdjIAp+fltvYdpRcrXlu208pbbO0++wj9pv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\nNGBTBNdKZpWmkYuQmLMIM8ewkzPy0LR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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z_9ag1w6eY9L",
        "colab_type": "code",
        "outputId": "b8dd44d6-3444-4cc5-a8ad-c95ebe4a6d16",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "# Now, let's define a function for creating the points on our parabola\n",
        "def create_para(x,a,n,xv,yv):\n",
        "    y = a * (x - xv) ** n + yv\n",
        "    return y\n",
        "\n",
        "# Now, lets create the parabola 3(x - 2)^2 + 1\n",
        "a = 3\n",
        "n = 2\n",
        "xv = 2\n",
        "yv = 1\n",
        "y = create_para(x,a,n,xv,yv)\n",
        "\n",
        "# Now, let's plot the line\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Parabola')\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7ukSaLt7eY9R",
        "colab_type": "text"
      },
      "source": [
        "You may have noticed that, in the code above, we did not __define__ x like we did when we created the line. This is because we already __defined__ x in another code block, so the kernel already has a __value__ assigned to x (the numbers in the range (-10,10))."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c5evkoJteY9S",
        "colab_type": "text"
      },
      "source": [
        "Once again, let's plot some points on the graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B0IFM2XpeY9U",
        "colab_type": "code",
        "outputId": "2e2fa906-a17f-4cee-9211-b232fcccf189",
        "colab": {}
      },
      "source": [
        "# Create two points in the range -10 < x < 10\n",
        "x_pt1 = -2\n",
        "dx = 3\n",
        "x_pt2 = x_pt1 + dx\n",
        "y_pt1 = create_para(x_pt1,a,n,xv,yv)\n",
        "y_pt2 = create_para(x_pt2,a,n,xv,yv)\n",
        "\n",
        "# Plot the points, along with the original function, on a graph\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.plot(x_pt1,y_pt1,'r.') # Plot the points as red dots\n",
        "plt.plot(x_pt2,y_pt2,'r.') \n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Parabola with Two Points')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jdxQRkUqhAlFJerZuwHnHteb1b9axMzPb7zgiIhWmAlGJbj31GPILHM/ocuAiUgOoQFSi9k3r8cuBbXn7u41s3H3I7zgiIhWiAlHJfnVyV2KijSenrvY7iohIhahAVLIWDeowdmgHPli8lVXbM/2OIyJSbioQYXDD8M4kxsfwl8+1FSEi1ZcKRBg0Sohj/PDOfLlyJws27PE7johIuahAhMlVJ3QgKTGexz5brZsKiUi1pAIRJglxMdw8qgtz1+1hRlqG33FERMpMBSKMLh7UjuTGdXn881UU6qZCIlLNqECEUVxMFL855RiWbcnkk2Xb/I4jIlImKhBhdn6/NhzTIpEnv/iB/ALdVEhEqg8ViDCLjjJ+e1o31mYc5N0Fm/2OIyJSaioQVeDUni3o164Rf52WRnZegd9xRERKJWwFwszqmNl3ZrbYzJab2f3e8I5mNtfM0szsHTOL84bHe/3p3vgO4cpW1cyM20/vxrb92fx9zga/44iIlEo4tyBygFHOuWOB44DRZjYYeBR4yjnXFdgLXONNfw2w1znXBXjKm67GGNo5iRO7JvFcajoHsnVTIRGJfGErEC4gy+uN9R4OGAW86w2fBJzvdZ/n9eONP9nMLFz5/HD76d3YeyiPF79e63cUEZESWTh/5Wtm0cACoAvwHPA4MMfbSsDM2gKfOud6m9kyYLRzbrM3bg1wvHMuo8g8xwHjAFq0aJEyefLkcmXLysoiMTGxfC+sAl5cnM28HQU8NKwuzRP+tz77laskylU2kZoLIjebcpVNRXKNHDlygXNuQIkTOufC/gAaAanAiUB60PC2wFKvezmQHDRuDdD0aPNNSUlx5ZWamlru51bEtn2HXY/ff+rGvTEv5Hi/cpVEucomUnM5F7nZlKtsKpILmO9Kse6ukrOYnHP7gOnAYKCRmcV4o5KBrV73Zq9g4I1vCNS4K921bFiHm0Z24fPlO5ilS3CISAQL51lMzcyskdddFzgFWElgS2KMN9lY4AOve4rXjzf+K6/S1TjXDOtIuyYJ3P/hcvL04zkRiVDh3IJoBaSa2RJgHjDVOfcRcCdwq5mlA02BV73pXwWaesNvBe4KYzZf1YmN5t6zepC2M0unvYpIxIopeZLycc4tAfqFGL4WGBRieDZwYbjyRJpTe7bgxK5JPDn1B849tjVNE+P9jiQi8hP6JbVPzIw/ntOTw7kF/OWLH/yOIyLyP1QgfNSleX2uGNKByfM2smzLfr/jiIj8hAqEz245pStNEuK4b8py3XlORCKKCoTPGtaN5fbTuzF/w16mLN5a8hNERKqICkQEuHBAW3q3acDDn6wiJ19bESISGVQgIkB0lHHfOb3YnpnNR2t1IT8RiQwqEBFiQIcmnH9caz5dn8fG3Yf8jiMiogIRSe46owfRBg9+vMLvKCIiKhCRpGXDOpzTKZYvVug6TSLiPxWICHNah1hdp0lEIoIKRISJi7Yfr9P05re6TpOI+EcFIgIduU7TU1/+wO6sHL/jiEgtpQIRgXSdJhGJBCoQEUrXaRIRv6lARDBdp0lE/KQCEcF0nSYR8ZMKRIQLvk7Todx8v+OISC2iAhHhgq/T9HzqGr/jiEgtogJRDRy5TtNLM9fqOk0iUmVUIKqJu87oQUyUcf+HOmAtIlVDBaKaaNmwDreeegzTVu3UAWsRqRIqENXIVSd05Ni2jbj/wxX6hbWIhJ0KRDUSHWU8PqYvB7LzuO9DXRJcRMJLBaKaOaZFfSaM7MqHi7cydcUOv+OISA2mAlEN3TCiM91b1uee95ey/7BuUSoi4aECUQ3FxUTx2Ji+ZGTl8NDHK/2OIyI1lApENdU3uRHXndSJd+Zv0t3nRCQsVCCqsd+ccgwdk+px13tLOJijy3CISOVSgajG6sRG8+jP+7J572Ee/3y133FEpIZRgajmBnVswhVD2jPp2/Us2LDH7zgiUoMUWyDM7BMz61B1UaS87hjdndYN63LHu0vIzivwO46I1BBH24KYCHxhZveYWWwV5ZFySIyP4eGf9WHNroM881Wa33FEpIYotkA45/4J9AMaAPPN7LdmduuRR5UllFI56ZhmjElJ5oWv1+oWpSJSKUo6BpEHHATigfpFHhJhfn9WT5rUi+OOd5eQV1DodxwRqeaOdgxiNLAISAD6O+f+6Jy7/8ijyhJKqTVMiOWB83qzYlsmL81Y63ccEanmjrYFcQ9woXPuLuec7lJTTYzu3ZKz+rTir1+mkb7zgN9xRKQaO9oxiBOdc8urMoxUjvvO7UVCfDR3vLuEgkLdXEhEyidsv4Mws7ZmlmpmK81suZnd4g1vYmZTzSzN+9vYG25m9rSZpZvZEjPrH65sNV2z+vH88ZyefL9xH5Nmr/c7johUU+H8oVw+cJtzrgcwGLjJzHoCdwHTnHNdgWleP8AZQFfvMQ74Wxiz1XjnH9eGkd2a8fjnq3UfaxEpl7AVCOfcNufc9173AWAl0AY4D5jkTTYJON/rPg94wwXMARqZWatw5avpzIw/X9CH6Cjj7veX6D7WIlJmVhUrDu8X2TOA3sBG51yjoHF7nXONzewj4BHn3Cxv+DTgTufc/CLzGkdgC4MWLVqkTJ48uVyZsrKySExMLNdzw6myc6VuzGPSilyu6hXH8Lbl/71jbWmvyhKpuSBysylX2VQk18iRIxc45waUOKFzLqwPIBFYAPzM699XZPxe7+/HwLCg4dOAlKPNOyUlxZVXampquZ8bTpWdq6Cg0P3yxdmu9x8+c9v2HS73fGpLe1WWSM3lXORmU66yqUguYL4rxfo7rBfr8y7R8W/gLefce97gHUd2HXl/d3rDNwNtg56eDGwNZ77aICrKePTnfckrLOSe95dqV5NINXc4t4DLXpnLyt3hv+5aOM9iMuBVYKVz7smgUVOAsV73WOCDoOFXeGczDQb2O+e2hStfbdK+aT3uOL0701bt5I1vN/gdR0Qq4E8fLWdWegb5VXAKezi3IE4ALgdGmdki73Em8AhwqpmlAad6/QCfAGuBdOBl4MYwZqt1rjqhA6O6N+fPH6/UtZpEqqkpi7fy9nebuGFEZ/o0iwn78sJ5FtMs55w55/o6547zHp8453Y75052znX1/u7xpnfOuZucc52dc31ckYPTUjFmxl8uPJYm9eK4+e2FZOkOdCLVyvqMg/zuvaX0b9eIW089pkqWqRsG1SJN6sXx9MX92LD7IPfqeIRItZGTX8DNby8kyuDpi/sRG101q24ViFpmUMcm/PqUY/jPoq38a8Fmv+OISCk8+ulqlm7Zz+MXHkty44QqW64KRC1008guDO3clD9+sFwX9BOJcFNX7OC1b9Yxdkh7Tu/VskqXrQJRC0VHGf/3y+NIiIvmprcW6jalIhFq677D3P7uYnq1bsDdZ/ao8uWrQNRSzRvU4YlfHMvqHQf400cr/I4jIkXkFxTyq7cXkpdfyLOX9KdObHSVZ1CBqMVGdGvO+OGd+cfcjXy0RL9JFIkk//dlGvM37OXPF/ShY1I9XzKoQNRyt512DP3bNeLufy/VVV9FIsSstAyem57OhSnJnN+vjW85VCBqudjoKJ6+uB9mMOHt78nN172sRfy060AOv35nEZ2bJXL/eb18zaICISQ3TuCxMX1Zsnk/j322yu84IrVWYaHj1n8u4kB2Hs9d0p+EuPD/WvpoVCAEgNG9W3HFkPa8Mmsd01bu8DuOSK30t6/XMDMtgz+e04tuLev7HUcFQv7rd2f2oGerBtz2r8Vs23/Y7zgitcr89Xt4cuoPnNW3FRcPalvyE6qACoT8qE5sNM9e0o/c/EJueXsR+QU6HiFSFfYdyuVXby+kTaO6PPyzPgQuhu0/FQj5iU7NEvnzBb35bv0enp6W5ncckRrPOccd7y5hV1YOz1zcjwZ1yn/nx8qmAiH/44J+yYxJSeaZ1HRmp2f4HUekRps0ez1frNjBnaO7c2zbRiU/oQqpQEhIfzqvF52S6nHLO4vIyMrxO45IjbRsy34e+mQVJ3dvzjXDOvod53+oQEhICXExPHtJf/YfzuM37yyiUJcGF6lUWTn5TPjH9zSpF8fjFx4bMccdgqlASLF6tGrAH87uycy0DD5dl+d3HJEawznHPe8vZeOeQzx9cT+a1IvzO1JIKhByVJce346z+rTi32l5fKPjESKV4o1vN/DBoq385pRjGNSxid9xiqUCIUdlZjzy8z60qmeM//sC3T9CpIJSV+3k/g+Xc0qP5tw4sovfcY5KBUJKVL9OLL/uX4f4mCiunjif3TpoLVIuK7dlMuEf39OjVQP+elE/oqMi77hDMBUIKZVmCVG8fMUAdmRmM+7NBbrJkEgZ7czM5pqJ80isE8OrYwdSL97f6yyVhgqElFq/do158hfHsWDDXu54dwlOZzaJlMrh3AKufWM++w7n8erYgbRsWMfvSKWiAiFlclbfVtx+ejemLN7K/32pX1qLlKSw0PGbdxaxdMt+nr6oH73bNPQ7UqlF/jaORJwbR3RmfcZB/jotjQ5JCVzQL9nvSCIR69HPV/HZ8u38/uyenNKzhd9xykRbEFJmZsafL+jD4E5NuPPdpXy3bo/fkUQi0uTvNvLi12u5bHA7rj6hg99xykwFQsolLiaKFy5LIblxXa5/cz7rMw76HUkkonyTnsG9/1nG8GOacd85vSLyl9IlUYGQcmuUEMdrVw4E4OqJ89h3KNfnRCKRIX3nAcb/fQGdmyXy7CX9iImunqva6plaIkaHpHq8ePkANu89zPi/L9A9raXW252Vw1UT5xEfE82rVw6gfgRdvrusVCCkwgZ1bMKjY/owZ+0e7nl/qU5/lVorO6+AcW8uYGdmDq+MHUBy4wS/I1WIzmKSSnFBv2TWZxzyzmyqx00RfgkBkcp25MY/Czbs5flL+3NchN3boTxUIKTS/PqUrqzLOMjjn6+mQ9N6nNW3ld+RRKrMU1+mMWXxVu4c3Z0z+9SMz752MUmlMTMeG9OXAe0bc+s/F7Fw416/I4lUifcXbubpaWn8YkAy44d38jtOpVGBkEpVJzaaFy9PoUWDOlz3xnw27TnkdySRsPpu3R7ufHcpQzo15cHz+1TL01mLowIhla5pYjyvXTmQnPxCrpk0j8xs3WxIaqb1GQe5/s35JDepywuXpRAXU7NWqTXr1UjE6NI8kRcuS2HtroPc9Nb35Bfo9FepWfYdyuXqifMAeP3KgTRMqL6nsxZHBULC5oQuSfz5gt7MTMvg1+8sUpGQGmP/4TzGvvYdm/ce5qUrBtC+aT2/I4VF2AqEmb1mZjvNbFnQsCZmNtXM0ry/jb3hZmZPm1m6mS0xs/7hyiVV65cD23H3Gd35aMk2bpm8iDwVCanm9h/K4/JX57JiWybPX9qfgR0i95ahFRXOLYiJwOgiw+4CpjnnugLTvH6AM4Cu3mMc8Lcw5pIqdv3wztxzZg8+XrqNWyYvVJGQamvfoVwufXUOq7Yd4IXLUqrd1VnLKmwFwjk3Ayh6mc/zgEle9yTg/KDhb7iAOUAjM6sZJxILANed1Il7z+rBJ0u386u3VSSk+tl3KJdLX5nLD9uzePHyFE7uUbOLA1T9MYgWzrltAN7f5t7wNsCmoOk2e8OkBrn2xE784eyefLpsOxP+8b2u2yTVxt6DuVzy8lzSdmbx0hUpjOzevOQn1QAWzuvmmFkH4CPnXG+vf59zrlHQ+L3OucZm9jHwsHNuljd8GnCHc25BiHmOI7AbihYtWqRMnjy5XNmysrJITEws13PDqTbkmrohj7dW5tK/eTQ3HhdPTAVu3F4b2quyRWq2SM21fW8Wz62IZtvBQm7pF0+fZpFxAYqKtNfIkSMXOOcGlDihcy5sD6ADsCyofzXQyutuBaz2ul8ELg413dEeKSkprrxSU1PL/dxwqi25Js1e59rf+ZG7ZuI8l5NXUO751Jb2qkyRmi0Sc2UcyHYnPPCxO+aeT9zXq3f6HecnKtJewHxXinV4Ve9imgKM9brHAh8EDb/CO5tpMLDfebuipGa6YkgHHjivF1+u3MGNby0gJ7/A70giP5GRlcMlL89lxyHHq2MHctIxzfyOVOXCeZrr28C3QDcz22xm1wCPAKeaWRpwqtcP8AmwFkgHXgZuDFcuiRyXD+lOaiXEAAASp0lEQVTAg+f35suVO7nh79+rSEjECBSHOWzYc5DfpNRhWNckvyP5Imw705xzFxcz6uQQ0zrgpnBlkch12eD2RJnxu/eXMv7NBfztshTqxEb7HUtqsV0HAsVh095DvHblQHI3LSv5STWUfkktvrvk+HY88rM+pK7exfVvLiA7T1sS4o+dB7K5+OU5bN57mNevHMTQzrVzy+EIFQiJCBcNasdjP+/LjLRdXPfGfBUJqXI7M7O5+KU5bN13mIlXDWRI56Z+R/KdCoREjF8MbMujP+/LrPQMFQmpUjsys7nopTls25/NxKsGcXwnFQdQgZAI84sBbXl8zLHMSs/g2knzOZyrIiHhtX1/oDjsyMxm0tWDGNSx5l5bqaxUICTijElJ5okLj+WbNRlcM2meioSEzbb9h7nopW/ZdSCHN64ZVKMvvFceKhASkX7WP5knf3Esc9bu5qKXvmX7/my/I0kNs2zLfn7+/GwysnKZdPUgUtqrOBSlAiER64J+ybxwWQrpO7M459lZLNige1xL5ZiyeCtjXpiNAyaPG0xK+8Z+R4pIKhAS0U7r1ZL3bjyBurHRXPzSHP45f1PJTxIpRkGh49HPVvGrtxfSp01DpkwYRu82Df2OFbFUICTidWtZnykTTuD4Tk24490l3DdluS4XLmWWmZ3HtZPm8bfpa7jk+Ha8de1gmtWP9ztWRIuMyxKKlKBRQhyvXzmQRz5dxSuz1rF6+wGeu1Q3HpTSWbMri+vemM/G3Yd48PzeXDa4vd+RqgUVCKk2YqKjuPfsnvRo1YC731/Kuc/O4vqefqeSSJe6aie/enshcTFRvHXt8fqNQxloF5NUOz9PSeaf1w8hr6CQB+Yc5tOluvCv/C/nHM9PT+fqSfNo1zSBKTcPU3EoIxUIqZaOa9uIDycMo139KG5463ue/GI1hYXhu/mVVC+Hcwu4+e2FPPbZas7u25p3xw+lTaO6fseqdrSLSaqt5g3qcOegOkzd04Snv0pnxbYDPPXLY6lfJ9bvaOKjLfsOM+6N+azYlsmdo7szfngnzMp/18LaTFsQUq3FRhmP/rwv95/bi9TVO/nZ87NZn3HQ71jik7lrd3PuM7PYuOcQr40dyA0jOqs4VIAKhFR7ZsbYoR1485pBZGTlcO6zs/j6h11+x5Iq9uacDVz6ylwaJsTyn5tOYGT35n5Hqva0i0lqjKGdk5gyYRjXvTGfq17/jqfaHubcfT9gI0fCkCF+x5Mwyc0v5L4Pl/OPuRsZ2a0Zf724Hw20m7FSqEBIjdK2SQL/vmEozz/8JqfdMp7Cwnyi4uOxadNUJGqgNbuyuP1fi/l+4z5uHNGZ207rRnSUdilVFhUIqXHqxcfw27htuMJ8ogoLyc/OYcXf/0OfwYO1P7qGyMkv4IXpa3kuNZ26cdE8e0k/zu7b2u9YNY4KhNRINnIkFh+Py82lICqG+zKbEffyHB66oA+dmiX6HU8q4Lt1e7j7vSWs2XWQc49tze/P7qlLZoSJCoTUTEOGwLRp2PTpxJ40nAtjk3nok5WM/utMbh7ZheuHdyYuRudoVCf7D+XxyGcrefu7TSQ3rsvEqwYyopsORIeTCoTUXEOGwJAhRAEXAyf3aM6fPlzBE1N/YMrirTz8sz4M0A1iIp5zjo+WbOP+D1ew91Au407qxK9P6UpCnFZf4aavUFJrNK9fh2cv6c/rVw7kUG4BY174lt+9v5T9h/P8jibF2Lz3EFdPnMfNby+kVcM6fHDTCfzuzB4qDlVErSy1zsjuzfniNyfx1NQfeO2bdUxdsYP7zunFmX1a6iB2hMgvKGTi7PU88cUPmMEfzu7J2KEddIZSFVOBkFqpXnwM957dk/OOa8Pd7y/hpn98z8ndm/On83vrmj0+W7ZlP3e9t4RlWzL1nvhMu5ikVuuT3JD/3HgC957Vg9lrdnPqk1/z6qx1FOjCf1UuO9/x4EcrOPfZWezIzOH5S/vzytgBKg4+0haE1Hox0VFce2InTu/Vkt9/sIwHPlrBB4u28NAFfXQ7yirgnGP66l3cM+swu7PXccnx7bhzdHca1tWvof2mAiHiadskgdevHOidMbOcs5+Zxajuzbn2xI4M6dRUxycqWX5BIZ8t387LM9exeNM+Wtcz/jV+CAN1ZlnEUIEQCWJmnHNsa07q2oyJs9fzxrfrueTlufRu04DrTuzEmX1aERutPbMVcTAnn3/O38Srs9axee9h2jdN4E/n9aLV4XUqDhFGBUIkhIYJsdxySleuH96J977fwiuz1nLL5EU8+ukqrh7WkV8ObKv7TpTRjsxsJs5ez1tzNpCZnc+A9o2596yenNqzBdFRxvTp6/2OKEWoQIgcRZ3YaC45vh0XDWxL6uqdvDRjLQ9+vJK/fpnGRYPactUJHWmtg6hHtXJbJq/MXMeUxVsoKHSM7t2Sa0/sRP92jf2OJiVQgRAphago4+QeLTi5RwuWbN7HyzPX8do363n9m/Wc1bcV153YSQe0gzjnmJmWwcsz1zIzLYO6sdFcenx7rj6hI+2aJvgdT0pJBUKkjPomN+KZi/tx5+huvP7NeiZ/t5EPFm1lSKemjDupE8OPaeZ3RN/k5hcyZfFWXpm5llXbD9C8fjy3n96NS49vR6OEOL/jSRmpQIiUU3LjBH5/dk9+dXJXJn+3kde/Wc9VE+fRpXkiw5rl0Scrh6aJteMqo5v2HOLDJVuZNHs9OzJz6NaiPo+P6cu5x7UmPiba73hSTioQIhXUsG4s1w/vzNXDOvLxkm28NGMtE5fnMnH5l/Rq3YBhXZM4sUszBnRoTJ3YmrGyzMzO49s1u5mZtotZaRms330IgBO7JvHYmGM5qWuSTguuAVQgRCpJbHQU5/drw3nHteb1KV9xqH47ZqZl8Nqsdbz49VriY6IY1LEJJ3ZNYliXZvRoVb/arETzCgpZvGkfM9IymJW2i8Wb91NQ6EiIi2ZIp6aMHdqB4cc00702ahgVCJFKZmZ0ahjNiBFdmTCqKwdz8pm7bjcz0zKYlZbBQ5+sAlaRlBjHsC5JDOvajBO7JtGiQR2/o//IOce6jIPMTMtgZloGc9buJisnnyiDPsmNuHFEZ4Z1SaJfu8a6r0YNFlEFwsxGA38FooFXnHOP+BxJpMLqxccwqnsLRnVvAcC2/YeZlZbBrPTAyvc/i7YC0LV5Iid2bcaZWevovHw+8aeOou5Jw8K+leGcI/NwPruycli5LfPHbFv2HQagbZO63o8HkxjaOYmGCfr9R20RMQXCzKKB54BTgc3APDOb4pxb4W8ykcrVqmFdLhzQlgsHtKWw0LFye2ClPDMtg2X//ozb37qb2IJ88h59iIsve5jN3Y8jKTGepMR4mtWPp1liHEn1438cluT114+P+bGYOOfYdyiPjKwcdmXlkJGVS8aBQPeytBwmrfsuMCwrh91ZueQWFP6Yr36dGIZ2bsr4EZ05qWsS7ZvW86upxGcRUyCAQUC6c24tgJlNBs4DVCCkxoqKMnq1bkiv1g25fnhn8rZ/SUxhAeYKiSos4PrCTXzQfiQZWbls3nuIRZv2svtgLi7ExWbjY6JISownv7CQ3Vm55Ie4Im1MlJEYC21cDkmJ8XRrWf/HItOsfjztmiTQp01DYnQ5EQHMhfqk+cDMxgCjnXPXev2XA8c75yYUmW4cMA6gRYsWKZMnTy7X8rKyskhMjLwDaspVNjUtV4Plyzn2ttuwvDxcbCyLn3iCzF69fjJNoXMcyIXMXMf+HMf+nEIyc2F/jiMz1xFt0CDOaBBvNIwzGsb/tzshFg4dPFij2izcamKukSNHLnDODShxQudcRDyACwkcdzjSfznwzNGek5KS4sorNTW13M8NJ+UqmxqZa/Zs5x56KPA3DGpkm4VRTcwFzHelWC9H0i6mzUDboP5kYKtPWUT8M2RI4CHis0ja0TgP6GpmHc0sDrgImOJzJhGRWititiCcc/lmNgH4nMBprq8555b7HEtEpNaKmAIB4Jz7BPjE7xwiIhJZu5hERCSCqECIiEhIKhAiIhKSCoSIiIQUMb+kLg8z2wVsKOfTk4CMSoxTWZSrbJSr7CI1m3KVTUVytXfOlXjrw2pdICrCzOa70vzUvIopV9koV9lFajblKpuqyKVdTCIiEpIKhIiIhFSbC8RLfgcohnKVjXKVXaRmU66yCXuuWnsMQkREjq42b0GIiMhRqECIiEhINbpAmNmFZrbczArNbECRcXebWbqZrTaz04t5fkczm2tmaWb2jncZ8srO+I6ZLfIe681sUTHTrTezpd508ys7R4jl3WdmW4KynVnMdKO9Nkw3s7uqINfjZrbKzJaY2ftm1qiY6aqkvUp6/WYW773H6d5nqUO4sgQts62ZpZrZSu/zf0uIaUaY2f6g9/cP4c7lLfeo74sFPO211xIz618FmboFtcMiM8s0s18XmabK2svMXjOznWa2LGhYEzOb6q2LpppZ42KeO9abJs3MxlY4TGnuKlRdH0APoBswHRgQNLwnsBiIBzoCa4DoEM//J3CR1/0CcEOY8z4B/KGYceuBpCpsu/uA35YwTbTXdp2AOK9Ne4Y512lAjNf9KPCoX+1VmtcP3Ai84HVfBLxTBe9dK6C/110f+CFErhHAR1X1eSrt+wKcCXwKGDAYmFvF+aKB7QR+SOZLewEnAf2BZUHDHgPu8rrvCvW5B5oAa72/jb3uxhXJUqO3IJxzK51zq0OMOg+Y7JzLcc6tA9KBQcETmJkBo4B3vUGTgPPDldVb3i+At8O1jDAYBKQ759Y653KByQTaNmycc1845/K93jkE7jzol9K8/vMIfHYg8Fk62Xuvw8Y5t805973XfQBYCbQJ5zIr0XnAGy5gDtDIzFpV4fJPBtY458p7hYYKc87NAPYUGRz8OSpuXXQ6MNU5t8c5txeYCoyuSJYaXSCOog2wKah/M//7D9QU2Be0Mgo1TWU6EdjhnEsrZrwDvjCzBWY2Low5gk3wNvNfK2aTtjTtGE5XE/i2GUpVtFdpXv+P03ifpf0EPltVwtul1Q+YG2L0EDNbbGafmlmvKopU0vvi92fqIor/kuZHex3Rwjm3DQJfAIDmIaap9LaLqBsGlYeZfQm0DDHqHufcB8U9LcSwouf7lmaaUillxos5+tbDCc65rWbWHJhqZqu8bxrldrRcwN+ABwi85gcI7P66uugsQjy3wudNl6a9zOweIB94q5jZVHp7hYoaYljYPkdlZWaJwL+BXzvnMouM/p7AbpQs7/jSf4CuVRCrpPfFz/aKA84F7g4x2q/2KotKb7tqXyCcc6eU42mbgbZB/cnA1iLTZBDYvI3xvvmFmqZSMppZDPAzIOUo89jq/d1pZu8T2L1RoRVeadvOzF4GPgoxqjTtWOm5vINvZwMnO2/na4h5VHp7hVCa139kms3e+9yQ/919UOnMLJZAcXjLOfde0fHBBcM594mZPW9mSc65sF6UrhTvS1g+U6V0BvC9c25H0RF+tVeQHWbWyjm3zdvltjPENJsJHCs5IpnA8ddyq627mKYAF3lnmHQk8E3gu+AJvBVPKjDGGzQWKG6LpKJOAVY55zaHGmlm9cys/pFuAgdql4WatrIU2e97QTHLmwd0tcDZXnEENs+nhDnXaOBO4Fzn3KFipqmq9irN659C4LMDgc/SV8UVtcriHeN4FVjpnHuymGlaHjkWYmaDCKwLdoc5V2nelynAFd7ZTIOB/Ud2rVSBYrfi/WivIoI/R8Wtiz4HTjOzxt4u4dO8YeVXFUfl/XoQWLFtBnKAHcDnQePuIXAGymrgjKDhnwCtve5OBApHOvAvID5MOScC44sMaw18EpRjsfdYTmBXS7jb7k1gKbDE+3C2KprL6z+TwFkya6ooVzqB/ayLvMcLRXNVZXuFev3AnwgUMIA63mcn3fssdaqCNhpGYNfCkqB2OhMYf+RzBkzw2mYxgYP9Q6sgV8j3pUguA57z2nMpQWcfhjlbAoEVfsOgYb60F4EitQ3I89Zf1xA4bjUNSPP+NvGmHQC8EvTcq73PWjpwVUWz6FIbIiISUm3dxSQiIiVQgRARkZBUIEREJCQVCBERCUkFQkREQlKBEKkkFriK6joza+L1N/b62/udTaQ8VCBEKolzbhOBS5Q84g16BHjJ+XjhN5GK0O8gRCqRd4mLBcBrwHVAPxe40qtItVPtr8UkEkmcc3lmdjvwGXCaioNUZ9rFJFL5ziBwqYTefgcRqQgVCJFKZGbHAacSuBvab6r4ZjcilUoFQqSSeFf7/BuB+y9sBB4H/uJvKpHyU4EQqTzXARudc1O9/ueB7mY23MdMIuWms5hERCQkbUGIiEhIKhAiIhKSCoSIiISkAiEiIiGpQIiISEgqECIiEpIKhIiIhPT/NopcLyZ1C0EAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qQ-yaBOgeY9Z",
        "colab_type": "text"
      },
      "source": [
        "Now that we have two points plotted on our parabola, we can estimate the derivative at the first point by plotting the __secant line__ going through the two points. This estimation will become more accurate (i.e. the secant line will converge to the __tangent line__ through the first point). This procedure is shown in the figure below:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P9sAPgOBeY9b",
        "colab_type": "text"
      },
      "source": [
        "![SlopeUrl](https://i.stack.imgur.com/3snPJ.gif \"slope\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8nABQntneY9c",
        "colab_type": "text"
      },
      "source": [
        "Now, let's plot the __secant line__ through those two points on our parabola."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jc72i5VReY9e",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Function for finding the equation of a line through two points\n",
        "def line2pts(x,P0,P1):\n",
        "    y = (x-P0[0])*(P1[1]-P0[1])/(P1[0]-P0[0])+P0[1]\n",
        "    return y\n",
        "\n",
        "# Plot the functions and points\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.plot(x_pt1,y_pt1,'r.') # Plot the points as red dots\n",
        "plt.plot(x_pt2,y_pt2,'r.') \n",
        "plt.plot(x,line2pts(x,(x_pt1,y_pt1),(x_pt2,y_pt2)),'g') # Plot the secant line as a green line\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Parabola and a Secant Line through Two Points')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PO7xJ0gSeY9h",
        "colab_type": "text"
      },
      "source": [
        "Take a moment to return to the code block where __dx__ was defined; try increasing and decreasing the value of dx. What happens to the secant line? "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iDmQQwKheY9i",
        "colab_type": "text"
      },
      "source": [
        "Now, let's plot the __derivative__ of our parabola. The __derivative__ of a parabola is a line, and each value represents the change in y over time at a specific point in time."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jXwk7y-beY9j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Function for finding the derivative of a parabola\n",
        "def derive_para(x,a,n,xv):\n",
        "    dy_dx = n * a * (x - xv)\n",
        "    return dy_dx\n",
        "\n",
        "dy_dx = derive_para(x,a,n,xv)\n",
        "\n",
        "# Plot the functions and points\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.plot(x,dy_dx,'o') # Plot the derivative of the parabola as an orange line\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Parabola and its Derivative')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uBMGLDtReY9o",
        "colab_type": "text"
      },
      "source": [
        "Cool! What about the __integral__ of a parabola? Taking the integral of a parabola may be viewed as the opposite of taking the derivative; so the integral of our parabola is going to be a __cubic__ function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NB_-ma1ceY9p",
        "colab_type": "code",
        "outputId": "86807adc-ee2e-49b7-e770-faa2d280ad76",
        "colab": {}
      },
      "source": [
        "# Function for finding the integral of a parabola\n",
        "def integrate_para(x,a,n,xv,yv):\n",
        "    Y = (a / (n + 1)) * (x - xv) ** (n + 1) + yv * x\n",
        "    return Y\n",
        "\n",
        "Y = integrate_para(x,a,n,xv,yv)\n",
        "\n",
        "# Plot the functions and points\n",
        "plt.figure()\n",
        "plt.grid()\n",
        "plt.plot(x,y)\n",
        "plt.plot(x,Y,'g') # Plot the integral of the parabola as an green line\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title('Plotting a Parabola and its Integral')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "abDXAgjeeY9u",
        "colab_type": "text"
      },
      "source": [
        "The integral of our parabola represents the area under the parabola at each point in time. The formula for integration is derived from a __Riemann Sum__ that begins by estimating the area under a curve by dividing the area into rectangles of width __w__, then shrinking w so that the rectangles are infintesimally small. This process is shown in the gif below."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YNm4LkQAeY9v",
        "colab_type": "text"
      },
      "source": [
        "![IntegralUrl](https://thumbs.gfycat.com/HilariousPhysicalAttwatersprairiechicken-size_restricted.gif \"integral\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fBOQ3gwa8O4b",
        "colab_type": "text"
      },
      "source": [
        "## Congratulations! You've completed the notebook, and should have a better understanding of how to plot different functions in Python."
      ]
    }
  ]
}