Quadratics – Equations and Functions

• A Quadratic Equation is an equation that can be written in the form

2 0ax bx c , , and are real numbers, 0a b c a

• Example 1:

The following is an example of a quadratic equation:25 3 4 0x x

• Example 2:

The following is another example of a quadratic equation, since it can be simplified and put into the general form of a quadratic equation.

2 28( 3) 2 4 1x x x 2 2

2

8 24 2 4 1

7 28 3 0

x x x x

x x

• A Quadratic Function is a function that can be written in the form

2( )f x ax bx c

The following is an example of a quadratic function:

• Example 3:

2( ) 5 3 4f x x x

• Note the difference between a quadratic equation and a quadratic function.

Quadratic Equation Quadratic Function

2 0ax bx c 2( )f x ax bx c

We usually solve quadratic equations.

We usually graph or evaluate quadratic functions.