1. A baseball is thrown directly upward with an initial velocity of 96 feet per second
from an initial height of 7 feet. The height
of the ball (in feet) after t seconds is given
by the formula h(t) = -16 t + 96t + 7.
a) After how many seconds will the ball
reach its maximum height?
b) What is that maximum height?

a) The ball reaches it's maximum height after 3 seconds.

b) The maximum height of the ball is of 151 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

Where

If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is .

In this question:

The height of the ball is modeled by:

So a quadratic equation with

a) After how many seconds will the ball reach its maximum height?

t-value of the vertex. So

The ball reaches it's maximum height after 3 seconds.

b) What is that maximum height?

h of the vertex.

The maximum height of the ball is of 151 feet.

answer: 91

step-by-step explanation:

b) well because you get well