Answer:
The maximum height that the football reached = 5.4 yards (16.2 feet)
Explanation:
The initial location of the ball = 15 yard line
The final location of the ball = 35 yard line
The equation of the ball's motion can be modeled as follows;
y = -0.054·(x - h)·(x - k)
Where;
h and k are the x-intercepts which are the points where the ball lands or where the ball is in contact with the ground
Given that the kicker kicks the ball from the ground on the 15 yard line and the ball lands on the ground at the 35 yard line, we can write
h = 15 yard line
k = 35 yard line
Therefore;
y = -0.054·(x - 15)·(x - 35) = -0.054·x² + 2.7·x-28.35
The maximum height is found by differentiating the function with respect to x and equating the result to 0 as follows;
d(-0.054·x² + 2.7·x-28.35)/dx = 2.7 - 0.108·x = 0
x = 2.7/0.108 = 25
Therefor, at the maximum point, we have;
x = 25
∴ y = -0.054·(25 - 15)·(25 - 35) = -0.054×10×(-10) = 5.4
The maximum height that the football reached = 5.4 yards = 16.2 feet.