Identifying The Extreme Values Of Quadratic Functions Worksheet With Answer Key - Math 11011 College Algebra, Kent State University Page 3
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5Extreme values of quadratic functions, page 3
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(c) f (x) = 2x
3x + 1
(d) f (x) =
x
8x + 7
Here, we know that a = 2, b =
3
Here, we have a =
1, b =
8
and c = 1. Since a > 0, we know
and c = 7. Since a < 0, we know
that the y coordinate of the vertex
that the y coordinate of the vertex
is a minimum. However, to find the
is a maximum. However, to find the
y coordinate of our vertex we first
y coordinate of our vertex we first
need to find the x coordinate of the
need to find the x coordinate of the
b
b
vertex by using x =
.
vertex by using x =
.
2a
2a
b
b
x =
x =
2a
2a
3
8
=
=
2(2)
2( 1)
3
8
=
=
4
2
3
=
4
=
4
Now that we have the x coordinate, we
Now that we have the x coordinate, we
can find the y coordinate of the vertex
can find the y coordinate of the vertex
by finding f ( 4).
3
by finding f
.
4
2
f ( 4) =
( 4)
8( 4) + 7
2
3
3
3
f
= 2
3
+ 1
4
4
4
=
16 + 32 + 7
9
9
= 23
= 2
+ 1
16
4
9
9
=
+ 1
Maximum = 23
8
4
9
18
8
=
+
8
8
8
1
=
8
1
Minimum =
8
NOTE: you can also solve the above prob-
lems by placing the quadratic in standard
form and identifying the y coordinate that
way.
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