Question

Dario is the kicker for his high school football team. The path of the football when kicked can be represented by the quadratic function y = -16x^{2} + 85x

, where x is the horizontal distance (in feet) and y is the height (in feet). How far does Dario kick the football? Express your answer as a decimal rounded to the nearest hundredth.

Answer 1

To find the horizontal distance the football travels, we need to find the maximum value of the quadratic function y = -16x^2 + 85x, which occurs at the vertex of the parabola.

The x-coordinate of the vertex is given by -b/2a, where a = -16 and b = 85:

x = -b/2a = -85/(2*(-16)) = 2.66

So the football travels a horizontal distance of approximately 2.66 feet when kicked.

To check that this is the maximum distance, we can find the value of y at x = 2.66:

y = -16(2.66)^2 + 85(2.66) = 113.56

So the maximum height reached by the football is approximately 113.56 feet.

Therefore, Dario kicks the football a horizontal distance of approximately 2.66 feet.