A ball is thrown upward and outward from a height of 77 feet. the height of the ball, f (x), in feet, can be modeled by f left parenthesis x right parenthesis equals negative 0.2 x squared plus 1.4 x plus 7f (x) = - 0.2x2+1.4x+7 where x is the ball's horizontal distance, in feet, from where it was thrown. use this model to solve parts (a) through (c).

From the given function modeling the height of the ball:

f (x) = - 0.2x^2+1.4x+7

A] The maximum height of the ball will be given by:

At max height f' (x) = 0

from f (x),

f' (x) = - 0.4x+1.4

solving for x we get:

-0.4x=-1.4

x=3.5ft

thus the maximum height would be:

f (3.5) = - 0.2 (3.5) ^2+1.4 (3.5) + 7

f (3.5) = 9.45 ft

b]

How far from where the ball was thrown did this occur:

from (a), we see that at maximum height f' (x) = 0

f' (x) = - 0.4x+1.4

solving for x we get:

-0.4x=-1.4

x=3.5ft

This implies that it occurred 3.5 ft from where the ball was thrown.

c] How far does the ball travel horizontally?

f (x) = - 0.2x^2+1.4x+7

evaluationg the expression when f (x) = 0 we get:

0=-0.2x^2+1.4x+7

Using quadratic equation formula:

x=-3.37386 or x=10.3739

We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.