Question

Terry throws a ball into a hoop that is 5 feet off the ground. The path of the ball can be modeled by the equation
y
=
−
x
2
+
4
x
+
5
, where x represents the horizontal distance traveled by the ball, in feet, and y represents the vertical height of the ball, in feet. Since the ball hoop is located 5 feet off the ground, you can use the equation
y
=
5
to model the position of the hoop. Determine the horizontal distance between Terry and the hoop.

Answer 1

Set y = 5 and solve −x^2 + 4x + 5 = 5:

−x^2 + 4x + 5 = 5
⇒ −x^2 + 4x = 0
⇒ −x(x − 4) = 0
⇒ x = 0 or x = 4.

Terry is at x = 0 and the hoop is at x = 4, so the horizontal distance is 4 feet.