finding height of the ball

Question

Jose threw a football to his friend Carmen. 

The height, h (in feet), of the ball above the ground at any given time, t, is given by the function h(t)=−16t2+40t+6.

How long will it take for Carmen to catch the ball if she catches it 4 feet above the ground?

Also, what is the highest the ball reaches?

Explain how you determined your answers and what graph used to find the solution.

Answer 1

Hello, Dotty,

I hope someone else can help with the algebraic solution. I simply graphed the equation and one can see that the football will be at the 4 ft height after 2.25 seconds, which seems fast for me. Perhaps Jose shouldn't list football as a career. Or perhaps mine should not include math.

Bob

Answer 2

For the first question you need to solve quadratic equation h(t)=4 for t.

If you have calculus you need to solve h'(t)=0 for t and then plug that value into h(t)

If you do not have calculus you need to know that the maximum of a quadratic equation

Ax² + Bx + C will occur when x=-B/2A and then plug that value into h(t).