Identifying The Extreme Values Of Quadratic Functions Worksheet With Answer Key - Math 11011 College Algebra, Kent State University Page 4
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2
3
4
5Extreme values of quadratic functions, page 4
2. During the annual frog jumping con-
3. A ball is thrown directly upward from
test at the county fair, the height of
an initial height of 50 feet.
If the
the frog’s jump, in feet, is given by
height, in feet, of the ball after t sec-
onds is given by
1
4
2
f (x) =
x
+
x.
3
3
2
f (t) =
16t
+ 40t + 50,
What
was
the
maximum
height
reached by the frog?
find the maximum height reached by
the ball.
1
Since f is a quadratic with a =
< 0,
3
the maximum height of the frog’s jump is
Since f is a quadratic with a =
16 < 0, the
found by identifying the y coordinate of
f (t) coordinate of the parabola’s vertex will
the parabola’s vertex. To do this note that
1
4
identify the maximum height. To find the
a =
, b =
and c = 0. First, we find the
3
3
b
t-coordinate of the vertex, we use t =
b
x coordinate by using
.
2a
2a
where a =
16 and b = 40.
b
x =
2a
b
t =
4
2a
3
=
1
2
40
3
=
2( 16)
4
3
=
2
40
=
3
32
= 2.
5
=
.
4
Next, we will have the maximum height once
we find f (2).
To find the maximum, we need to evaluate
5
f
.
1
4
4
2
f (2) =
(2)
+
(2)
3
3
1
8
=
(4) +
2
5
5
5
3
3
f
=
16
+ 40
+ 50
4
4
4
4
8
=
+
3
3
25
=
16
+ 50 + 50
16
4
=
.
3
=
25 + 100
= 75.
4
Maximum height of frog’s jump =
ft
3
Maximum height of ball = 75 feet
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