Identifying The Extreme Values Of Quadratic Functions Worksheet With Answer Key - Math 11011 College Algebra, Kent State University Page 2
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5Extreme values of quadratic functions, page 2
PROBLEMS
2
1. Find the maximum or minimum value
(b) f (x) =
2x
+ 8x + 9
of each quadratic function.
State
whether it is a maximum or minimum.
Here, we know that a =
2, b = 8
and c = 9. Since a < 0, we know
2
(a) f (x) = 3x
6x + 2
that the y coordinate of the vertex
is a maximum. However, to find the
y coordinate of our vertex we first
Here, we know that a = 3, b =
6
need to find the x coordinate of the
b
and c = 2. Since a > 0, we know
vertex by using x =
.
2a
that the y coordinate of the vertex
is a minimum. However, to find the
b
y coordinate of our vertex we first
x =
2a
need to find the x coordinate of the
b
vertex by using x =
.
8
2a
=
2( 2)
b
8
x =
=
2a
4
6
= 2
=
2(3)
Now that we have the x coordinate, we
6
=
can find the y coordinate of the vertex
6
by finding f (2).
= 1.
Now that we have the x coordinate, we
2
f (2) =
2(2)
+ 8(2) + 9
can find the y coordinate of the vertex
=
2(4) + 16 + 9
by finding f (1).
=
8 + 16 + 9
2
f (1) = 3(1)
6(1) + 2
= 17.
= 3
6 + 2
Maximum = 17
=
1.
Minimum =
1
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