{
  "icon" : "function",
  "id" : "1661D9E2-64BB-55ED-A505-F8AF2991DCBB",
  "lines" : [
    {
      "id" : "7C2A9059-DAEE-5884-ABCE-E006D590DE6A",
      "source" : "# Quadratic explorer"
    },
    {
      "id" : "33935178-E326-5D71-BF4D-00867977FF13",
      "source" : "\/\/ c stays at or below zero here, so the parabola always crosses the x-axis."
    },
    {
      "id" : "0D522DDE-EAB0-5885-8946-107F8FA23D19",
      "source" : "a = 1 in 0.5 … 3"
    },
    {
      "id" : "CBA8D31C-86C8-5EA8-AB49-A9BEBC2E427D",
      "source" : "b = -2 in -8 … 8"
    },
    {
      "id" : "270A6C60-0AF0-51D3-AC5F-C8D18E3DBEFF",
      "source" : "c = -3 in -8 … 0"
    },
    {
      "id" : "14D77A5D-53CB-5CF9-9EA7-D44DE69EE82C",
      "source" : "f(x) = a*x² + b*x + c"
    },
    {
      "id" : "2209C4C6-1137-554F-A0A1-FD3E2BA89375",
      "source" : "plot(f(x), x, -8, 8)"
    },
    {
      "id" : "62C941EF-208C-5D19-BE8A-9F417DF9CBF9",
      "source" : ""
    },
    {
      "id" : "9B84F5FD-3661-587F-AAB4-58BB00E44839",
      "source" : "# Vertex"
    },
    {
      "id" : "45A0EF92-5704-5F51-9C55-04AFE5765293",
      "source" : "vertex x = -b\/(2*a)"
    },
    {
      "id" : "A449BB9F-1043-59CD-A92E-7A09BDF234D3",
      "source" : "vertex y = f(vertex x)"
    },
    {
      "id" : "E93BE5B7-AE7C-599E-BF10-A5D080DA197C",
      "source" : ""
    },
    {
      "id" : "7DD95984-9672-50A8-9390-ADDEB3A6A3F6",
      "source" : "# Roots"
    },
    {
      "id" : "A0414CD0-90AD-5E4A-B05A-E7B6FF5FE495",
      "source" : "discriminant = b² - 4*a*c"
    },
    {
      "id" : "711DCBE7-7A8C-58B4-A9F2-79AC6DBF6C3C",
      "source" : "root one = (-b - sqrt(discriminant))\/(2*a)"
    },
    {
      "id" : "71098EBF-2AF4-5331-BC00-FE49F6BFAC38",
      "source" : "root two = (-b + sqrt(discriminant))\/(2*a)"
    },
    {
      "id" : "167289C8-2F12-52A4-8C81-8ED0909B8ED5",
      "source" : "f(root one) == 0"
    },
    {
      "id" : "9694CD7D-6ED7-5B82-8F34-D71537B27E60",
      "source" : "f(root two) == 0"
    }
  ],
  "numberStyle" : {
    "decimal" : ".",
    "grouping" : ",",
    "secondaryGroupSize" : 3
  },
  "title" : "Quadratic functions"
}