demo1_quadratic_equation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo 1: Quadratic Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Define a quadratic equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "solution2": "hidden",
    "solution2_first": true
   },
   "source": [
    "A quadratic equation can be written as:\n",
    "\\begin{equation}\\label{eq:quadratic_equation}\n",
    "a \\boldsymbol{x}^2 + b \\boldsymbol{x} + c = 0\n",
    "\\end{equation}\n",
    "where $\\boldsymbol{x}$ is the variable, and a, b, c are the coefficients.\n",
    "\n",
    "\\textbf{Task}: \n",
    "\n",
    "Define a function solve(a, b, c) to find the solution for Equation (1).\n",
    "\n",
    "If there is valid solution, return None.\n",
    "\n",
    "\\textbf{Code Format}:\n",
    "\n",
    "def solve(a, b, c):\n",
    "    \n",
    "    # Write your code here.\n",
    "    \n",
    "    if has_solution:\n",
    "        return x1, x2\n",
    "    else:\n",
    "        return None\n",
    "\n",
    "Noting that sqrt function in Numpy library can implement find the squared root of a variable. \n",
    "\n",
    "import numpy as np; np.sqrt(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "solution2": "hidden"
   },
   "source": [
    "Solutions for the quadratic equation:\n",
    "\n",
    "\\begin{equation}\\label{eq:}\n",
    "x = \\frac{-b \\pm \\sqrt{b^2-4ac}}{2a}\n",
    "\\end{equation}\n",
    "\n",
    "holds if $b^2-4ac \\geq 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "solution2": "hidden"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def solve(a, b, c):\n",
    "    b2_4ac = b**2 - 4*a*c\n",
    "    has_solution = b2_4ac >= 0 \n",
    "    if has_solution:\n",
    "        x1 = (-b + np.sqrt(b2_4ac))/(2*a)\n",
    "        x2 = (-b - np.sqrt(b2_4ac))/(2*a)\n",
    "        return (x1, x2)\n",
    "    else:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "solution": "shown",
    "solution2": "hidden",
    "solution2_first": true,
    "solution_first": true
   },
   "source": [
    "# 2. Plot the quadratic function (using matploblib library)\n",
    "Matploblib is a third-party library for data visualization in Python. \n",
    "\n",
    "Capable of plotting: Lines, Charts, Curves, Scatter, etc.\n",
    "\n",
    "\\textbf{Task}:\n",
    "Use Matploblib.pyplot to plot the curve for equation:\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "f(x) = ax^2 + bx + c\n",
    "\\end{equation}\n",
    "\n",
    "E.g. a = 1, b = -2, c = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "solution": "shown",
    "solution2": "hidden"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig = plt.figure(1)\n",
    "x = np.arange(-3.0, 5.0, 0.1)\n",
    "a, b, c = 1.0, -2.0, -3.0\n",
    "y = a*x**2 + b*x + c\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, [0 for _ in x])\n",
    "plt.legend(['y=f(x)', 'y=0'])\n",
    "\n",
    "x1, x2 = solve(a, b, c)\n",
    "plt.scatter([x1, x2], [0, 0], color='red', marker='o', s=50)\n",
    "plt.text(x1, 0.5, s='x1={:.2f}'.format(x1), size='large')\n",
    "plt.text(x2, 0.5, s='x2={:.2f}'.format(x2), size='large')\n",
    "\n",
    "plt.grid(True)\n",
    "plt.title('Solution for Quadratic Function')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:py36]",
   "language": "python",
   "name": "conda-env-py36-py"
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  "latex_envs": {
   "LaTeX_envs_menu_present": true,
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   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
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   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
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   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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    "r": {
     "delete_cmd_postfix": ") ",
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   "types_to_exclude": [
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