Identifying The Extreme Values Of Quadratic Functions Worksheet With Answer Key - Math 11011 College Algebra, Kent State University Page 5
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5Extreme values of quadratic functions, page 5
4. A toy rocket is launched of the top of a 150 foot cliff. If the height, in feet, of the rocket
t seconds after liftoff is given by
2
f (t) =
16t
+ 288t + 150,
find the maximum height of the rocket and the time it reaches its maximum height.
Since f is a quadratic with a =
16 < 0, the t coordinate of the parabola’s vertex will identify
the time the rocket reaches its maximum height and the f (t) coordinate of the vertex will give the
b
maximum height. We first find the time t by using t =
where a =
16 and b = 288.
2a
b
t =
2a
288
=
2( 16)
288
=
32
= 9.
Next, to find the maximum height, we evaluate f (9).
2
f (9) =
16(9)
+ 288(9) + 150
=
16(81) + 2592 + 150
=
1296 + 2592 + 150
= 1446.
Time to reach max height = 9 seconds
Maximum height of rocket = 1446 ft
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