(NEED ASAP) Quadratic Functions Math Problem

Question

The height, h (in feet), of a golf ball depends on the time, t (in seconds), it has been in the air. Sarah hits a shot off the tee that has a height modeled by the quadratic function f(h) = -16(t – 2.5)² + 100.

1. What is the maximum height of the golf ball? How long does it take for the golf ball to reach the maximum height?

2. What is the total flight time of the ball?

3. What is the domain of the function as it is applied to the actual situation? Make sure you use correct notation.

4. Suppose that the tee location was moved to a spot 20 feet higher up a hill. Sarah hit the exact same shot from that location. What effect does this change in height have on the quadratic function compared to the original model?

Answer 1

The function should say h(t) instead of f(h)

h(t) = -16(x - 2.5)² + 100 is in vertex form. That means you can read the vertex right from the equation. It is (2.5, 100). This means the highest the golf ball goes is 100 feet and that occurs after 2.5 seconds

Since the ball takes 2.5 seconds to reach that max height, it will take another 2.5 seconds to get back to the ground (remember that a parabola is symmetrical) so the total time in the air is 2.5 + 2.5 or 5 seconds.

The domain is t = 0 to t = 5. You can write this several ways so I'll leave it to you to write it the way you have learned. It could be 0 < t < 5 or it could be [0, 5] or something like these.

If she moved 20 feet up the hill, we would get something like this:

So it would be 20 feet higher at the top.