David Longshot is known for his long golf drives. At the driving range he hit a golf ball $250$ yards and estimated that the ball reached a maximum height of $15$ yards.

1. Use a quadratic function to model the path of the golf ball.

   Hint (a):

   Recall the quadratic equation:
   $f\left(x\right) = a\left(x − h\right)^{2} + k$

   Help (a):

   Use the maximum-point coordinates to replace some variables in the equation above.

   Substitute $\left(0, 0\right)$ for $x$ and $y$ to solve for the slope.

2. David’s brother, Dwayne, was also at the driving range and hit a ball according to the table below. Which ball traveled farther horizontally? Which ball went higher in the air?

   Horizontal distance (yd)	Height (yd)
   $0$	$0$
   $20$	$5.5$
   $60$	$13.5$
   $180$	$13.5$
   $220$	$5.5$

   Hint (b):

   Sketch Dwayne's projection and notice how much farther his ball can travel past $220$ yards.

   Partial Answer (b):

   David's ball traveled farther at $250$ yards while Dwayne's ball traveled $240$ yards.
   How high did Dwayne's ball go?