Question

Problem:
A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet,
can be modeled by
I
f(x)=-0.6x2 +2.7 x+6
where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to
solve parts (a) through (b).
a. What is the maximum height of the ball and how far from where it was thrown does this
occur? Place answer below, but you MUST show all work!
feet from the point of release.
The maximum height is feet, which occurs
(Round to the nearest tenth as needed)
b. How far does the ball travel horizontally before hitting the ground?
Place answer below, but you MUST show all work!
The ball travels
feet. (Round to the nearest tenth as needed).

Answer 1

The maximum height is 9.0 feet and the time to hit the ground is 4.5 seconds

How to determine the maximum height?

The function is given as:

f(x) = -0.6x^2 + 2.7x + 6

Differentiate

f'(x) = -1.2x + 2.7

Set to 0

-1.2x + 2.7 = 0

Subtract 2.7 from both sides

-1.2x = -2.7

Divide both sides by -1.2

x = 2.25

Substitute x = 2.25 in f(x) = -0.6x^2 + 2.7x + 6

f(2.25) = -0.6(2.25)^2 + 2.7(2.25) + 6

Evaluate

f(2.25) = 9.0

Hence, the maximum height is 9.0 feet

How to determine the time to hit the ground?

The time to hit the ground is twice the time to reach the maximum height.

In (a), we have:

x = 2.25

So, we have:

Time = 2 * 2.25

Evaluate

Time = 4.5

Hence, the time to hit the ground is 4.5 seconds

Read more about quadratic functions at:

https://brainly.com/question/1214333

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