How to Solve & Graph Quadratic Equations


Solving a quadratic equation typically involves factoring it as much as possible and determing the x intercepts and tip. One method of solving a quadratic equation is by graphing the equation. To graph, you must create a table of values, or plots, then place them on the graph accurately enough to draw an appropriate curve. Most quadratic equations are written in the form "y = ax^2 + bx +c" but they can also be written with the y at the end of the equation.

Things You'll Need

  • Graphing paper
  • Pencil
  • Write the equation in the traditional quadratic form of "ax^2 + bx + c = y." The equation might read "1x^2 + 2x + 0 = y."

  • Create a table of values by plugging in different x values. Start around -5 or -3 and move to around 3 or 5. Plug the value into the x spot of the equation and solve the equation to determine the y value. For example, plug in -1 for "1x^2 + 2x + 0 = y" to find "(1)(1) + (2)(-1) + 0= y" in which "y = 1-2" or -1. Write the point as (-1, -1). Repeat this process for all of the values.

  • Determine where the tip of the parabola lies by looking at the chart. The parabola lies at the place where y values repeat. For example, if the y value for x = 1 is the same as the y value for x = -1, the tip is between 1 and -1.

  • Graph the points on a sheet of graph paper. Plot (-1, -1) at the -1 x point and the -1 y point. Graph all of the remaining points. The shape should look like a curve.

  • Attempt to factor the equation to determine the x intercepts. The equation "1x^2 + 2x + 0 = y" factors to "x(x + 2) = y," meaning that at -2 and 0, y = 0. These are the x intercepts.

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