Quadratic Equations

A Summary of the Methods of Solving Quadratic Equations
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Quadratic equations are of the form where a, b and c are real numbers and .
. Quadratic equations have two solutions. It is possible that one solution may repeat.

Solving by Factoring

Some quadratic equations can be solved by factoring. Set the equation equal to zero and factor.

Example 1:
Solve by factoring:

Example 2:
Solve by factoring:

Solving by Graphing

Some quadratic equations can be solved by graphing. Setting the equation equal to zero will show the roots as locations on the x-axis.

Example 1: Solve by graphing:

Method 1: Set the equation equal to zero, if necessary. Find the roots using the ZERO command tool of the graphing calculator. For help with the calculator, click here.

Example 2: Solve by graphing:

Method 2: Graph each side of the equation separately. Use the INTERSECT command tool to find when the graphs cross. Repeat this process for both intersection points. For help with the calculator, click here.

Solving by Quadratic Formula

Quadratic Formula:

The solutions of some quadratic equations are not rational, and cannot be factored. For such equations, the most common method of solution is the quadratic formula. The quadratic formula can be used to solve ANY quadratic equation, even those that can be factored.
Be sure you know this formula!!!

Note: The equation must be set equal to zero before using the formula.

Example: