Question

With the given model: h=-0.045d^2+2d
where h is the height of the ball from the ground(in yards) and d is the horizontal distance of the ball(in yards) from its starting point.

A.)Pat is standing on the 17-yard line when the football passes over his head. How high up is the football at this point?

B.)The football is 8 yards above the ground when it passes over Billy. At what yard line is Billy standing when the football passes over his head?

Answer 1

for (a), we substitute 17 to d in the equation for the height,h:
h = -0.045d^2 + 2d
h = -0.045*(17^2) + 2(17)
h = 20.995 yards

for (b), we are given the height and we need to find the horizontal distance. substituting,
h = -0.045d^2 + 2d
8 = -0.045d^2 + 2d
0 = -0.045d^2 + 2d - 8
note that this is a quadratic equation and we can either factor it or use quadratic formula to solve for d,, here, let's just use quadratic formula:
d = [-b +- sqrt(b^2 - 4ac)]/(2a)
d = [-2 +- sqrt(2^2 - 4(-0.045)(-8))]/(2(-0.045))
d = [-2 +- sqrt(2.56)]/(-0.09)
d = [-2 +- 1.6]/(-0.09)
d = 40 yards
d = 4.44 yards
note that there are two answers. for the 4.44 yards, the ball is going up, while for the 40 yards, the ball is already going down.

hope this helps~ :)