Graph is a parabola. Either has a minimum or maximum point. That point is called a vertex. Use...

Graph is a parabola. Either has a minimum or maximum point. That point is called a vertex. Use transformations of previous section on x2 and -x2

to get graph of any quadratic function.

4.1 Quadratic Functions

Examplef(x) = x2: shift up 4 units and shift to the left 5 units

2x

Minimum value is

Standard Form

is form standard the)(For 2 cbxaxxf

khxaxf 2)()(

:and vertex, theis ),( where kh

Example 1

Graph the function: 5)3()( 2 xxf

Minimum value is

Example 2

Graph the function: 3)4()( 2 xxf

2x Maximum value is

Example 3

Find the maximum or minimum value of the function.

2414)( 2 xxxf khxa f(x) 2)(:form standard Need

Minimum value is

x-intercepts =

y-intercepts =

Find the maximum or minimum value of the function.

1163)( 2 xxxf

khxa f(x) 2)(:form standard Need

Maximum value is

Example 4

x value of the vertex

,:form general For the 2 cbxax f(x)

.2

at occurs vertex thea

bx

.2

is min)or (max valueextreme The

a

bf

Find the maximum or minimum value of the functions.

1163)( 2 xxxf

245)( 2 xxxg

Examples