introduction to quadratic functions objective: define, identify, and graph quadratic functions....
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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
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