Question

98 POINTS AND BRAINLIEST

A ball is thrown upward and outward from a height of 7 feet. The height of the​ ball, f(x), in​ feet, can be modeled by f(x) = -0.3x^2 + 2.1x + 7 where x is the​ ball's horizontal​ distance, in​ feet, from where it was thrown.

What is the maximum height of the ball and how far from where it was thrown does this​ occur?

Answer 1

Answer:

max height = 7.5 ft

1.3 ft far

Please check below for the detailed answer

Step-by-step explanation:

Given:

f(x) = −0.3x^2 + 2.1x + 7

a) To obtain the maximum height , find f'(x)

f'(x) = - 0.6x + 0.8 = 0

=> x = 0.8 / 0.6 = 1.33 feet

So f(x) is maximum at a horizontal distance of 1.33 ft

To find the max height , find f(1.33)

f(x) = −0.3x^2 + 2.1x + 7, plug in 1.33 for x

=> f(1.33) = −0.3(1.77) + 0.8(1.33) + 7 = 7.5 ft

So the answer is

Maximum height = 7.5 ft , and 1.3 ft far from where it was thrown.