College Algebra quadratic modeling

Question

A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by .

What is the rocket's maximum height? feet 

How long does it take for the rocket to reach its maximum height?

 seconds

After it is fired, the rocket reaches the ground at t= seconds

Answer 1

To find the maximum height, you need to find the vertex of the parabola represented by this quadratic equation. The equation is in standard form, i.e., f(x) = ax² + bx + c. If we call the vertex (h, k), then h = -b/2a

and k = f(h).

The value of k will be the maximum height. The value of h will tell how long it takes for the rocket to reach its maximum height.

To determine when the rocket returns to the ground, set the quadratic equation equal to zero and solve for t.