Quadratic Functions Worksheet - Lesson 36 Ma 152, Section 3.1, Purdue Math Page 7
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8Minimums and Maximums:
If a parabola opens upward, its vertex is the location of a relative minimum. If it opens downward, its
vertex is the location of a relative maximum. If the vertex is (h, k), the maximum of minimum value is
.
k
f h
( )
and it occurs when x h
Ex 6: For each quadratic function describe if it has a maximum or minimum, what the maximum or
minimum value is and where it occurs, and the domain and range of the function (using interval
notation).
2
a
)
f x
( )
3
x
12
x
11
1
2
b
)
g x
( )
x
4
x
6
2
2
Ex 7: Write an quadratic function (in standard form) that has the same shape as
, but with a
g x
( ) 2
x
vertex ( 3,12)
.
Finding a quadratic function using the vertex and a second point:
The equation for a quadratic function can be found if the vertex and one other point of the parabola is
2
known. Replace , , , and with the correct values and solve for
x y h
k
a
in ( )
f x
a x h
(
)
k
.
Ex 8: Find equation for each in standard form.
a
)
V
(2, 3),
P
(1, 4)
b
)
V
(9, 1), -intercept is 4
x
7
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