Introduction to Quadratic Functions

Objective: Define, identify, and graph quadratic functions. Multiply binomials

to produce a quadratic expression.

11 22 xxxx)1

11 22 xxxx 18111829 22 xxxxx)1 )2

11 22 xxxx

35134352074 22 xxxxx

18111829 22 xxxxx)1 )2

)3

11 22 xxxx

35134352074 22 xxxxx

18111829 22 xxxxx

4715451215 22 xxxxx

)1 )2

)3 )4

11 22 xxxx

35134352074 22 xxxxx

18111829 22 xxxxx

4715451215 22 xxxxx

9929632 22 xxxxx

)1 )2

)3

)5

)4

Quadratic Functions

• A quadratic function is any function that can be written in the form where . It is defined by a quadratic expression, which is an expression of the form , where .

)( 2 cbxaxxf 0a

2 cbxax 0a

Example 1

Example 1

You Try

• Let . Show that g represents a quadratic function. Identify a, b, and c when the function is written in the form .

)2)(52()( xxxg

)( 2 cbxaxxg

You Try

• Let . Show that g represents a quadratic function. Identify a, b, and c when the function is written in the form .

F O I L

)2)(52()( xxxg

)( 2 cbxaxxg

10542)2(5)2(2)2)(52( 2 xxxxxxxx

10,9,2

1092 2

cba

xx

Example 2

Example 2

Example 2

Try This

• Identify whether has a minimum value or maximum value at the vertex. Then, give the coordinates of the vertex.

142)( 2 xxxf

Try This

• Identify whether has a minimum value or maximum value at the vertex. Then, give the coordinates of the vertex. Maximum.

142)( 2 xxxf

Try This

• Identify whether has a minimum value or maximum value at the vertex. Then, give the coordinates of the vertex. Maximum.

142)( 2 xxxf

Try This

• Identify whether has a minimum value or maximum value at the vertex. Then, give the coordinates of the vertex.

223)( 2 xxxf

Try This

• Identify whether has a minimum value or maximum value at the vertex. Then, give the coordinates of the vertex. Minimum.

223)( 2 xxxf

Try This

• Identify whether has a minimum value or maximum value at the vertex. Then, give the coordinates of the vertex. Minimum.

223)( 2 xxxf

Example 3

Example 3

Example 3

Homework

• Page 278• 13-45 odd