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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