Quarterback Joe Tarkenton can throw a football downfield at a speed of 60 feet per second. When releasing the ball, his arm is 6 feet above ground. The height of the ball after seconds is given by the function: h(t)=−16^2+60+6. What is the maximum height of the football?

If the ball is not caught, how many seconds will it take to reach the ground after being thrown?

A: maximum height=3.58 feet; time=62.25 seconds

B: maximum height=62.52 feet; time=3.58 seconds

C: maximum height=62.25 feet; time=3.85 seconds

D: maximum height=3.85 feet; time=62.52 seconds

C: maximum height=62.25 feet; time=3.85 seconds

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 .

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

In this question:

The height of the ball, after t seconds, is given by the following equation:

Which is a quadratic equation with

Maximum height:

Since a < 0, we can find the maximum value of the function. We have that:

The maximum height is of 62.25 feet.

Seconds to reach the ground:

Since time is a positive measure, 3.85 seconds.

The correct answer is given by option C.

b. 2 and 4

step-by-step explanation: