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Quadratic Equations

Quadratic Equations

Author: Joshua Galvez

Solve quadratic equations in one variable.
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.

Grades 9-12

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Connections to Prior Knowledge

We've worked on linear equations. To learn about linear equations, click here.

y equals a x plus b

These equations had a constant rate of change, sometimes known as the slope.

Quadratic Equations have a variable rate of change; a variable slope. This is an example of a quadratic equation:

y equals a x squared plus b x plus c

Linear equation graphs were straight lines. Quadratic equation graphs are parabolas.

Quadratic Equations in Real Life

This video shows where we can see quadratic equations in the real world.

How to Complete the Square.

To learn how to complete the square when solving quadratic equations, click here.

Example of Completing the Square (Basic)

Example of Completing the Square (Advanced)

This is an example of completing the square.