Perry throws a tennis ball up into the air from the edge of a cliff. The height of the ball can be modeled by the function $y = -16x^2 + 64x + 80$, where $y$ represents the height in feet of the ball above ground at the bottom of the cliff, and $x$ represents the time in seconds after the ball is thrown.

1. How high is the ball when it is thrown? How do you know?

   Hint (a):

   If you sketch the curve, it is a downward-facing parabola. Where is the highest point?

2. What is the height of the ball three seconds after it is thrown? What is its height a half second after it is thrown? Show all work.

   Step (b):

   $y = -16(3)^2 + 64(3) + 80$
   $y = -16(0.5)^2 + 64(0.5) + 80$

3. When does the ball hit the ground? Write and solve an equation that represents this situation.

   Hint (c):

   The height of the ball when it hits the ground is $0$ feet.

   Step (c):

   Solve $0 = -16(x)^2 + 64(x) + 80$.

4. What is the domain of the function for this context?

   Hint (d):

   This is the time from when the ball is initially thrown until the time it hits the ground.