Question

A diver is standing on a platform 7 ft above the pool.

He jumps from the platform with an initial
upward velocity of 20 ft/s. Use the formula
h(t) =- 16+ + vt + s, where h is his height above the
water, t is the time, v is his starting upward velocity
and s is his starting height. What is the maximum
altitude that the diver reaches? Round to the nearest
whole number.

Answer 1

13 ft

Explanation:

We assume your height formula is intended to be ...

h(t) = -16t² +20t +7

This will have its maximum value at ...

t = -b/(2a) = -20/(2(-16)) = 5/8

The height at that time is ...

h(5/8) = (-16(5/8) +20)(5/8) +7 = 10(5/8) +7 = 106/8 = 53/4 = 13 1/4 . . . ft

To the nearest whole foot, the diver will reach a height of 13 ft above the pool.

_____

Additional comments

The standard form quadratic can be described as ...

f(x) = ax² +bx +c

The extreme value occurs at ...

x = -b/(2a)

This can also be written as ...

f(x) = (ax +b)x +c

which can make it easier to evaluate for some numerical value of x.