Study Island Help

Question

Dr. Peabody shot a rocket off the roof of a 42-foot tall building. After three seconds, the rocket reached its highest point of 96 feet.

Model this situation with a quadratic function, and use the graph to determine how many seconds it will take the rocket to hit the ground?

Answer 1

The graph would be an upside down parabola with a vertex (3, 96) and the other point on the graph is (0, 42).

I used the vertex form which is y=a(x-h)²+k of a quadratic equation to find a. By substitution 42 = a(0 - 3)² + 96 so a = -6. Next, I let y=0 since 0 is the rocket hitting the ground. Next I solved the equation 0 = -6(x - 3)² + 96 and x = 7. So it would take 7 seconds for the rocket to hit the ground.