Twinkle toes tony kick the football and it landed 100 feet from where he kicked it also reach a maximum height of 125 feet write an equation that models the path of the ball while it was in the air

The equation that models the path of the ball is y = 5·x - 0.05·x²

Step-by-step explanation:

The given information are;

The distance the football landed from where it was kicked = 100 feet

The maximum height the football reached =  125 feet

The equation that models the path of the ball is that of the equation of parabola in vertex form, given as follows;

y = a·(x - h)² + k

Where;

(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)

Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;

The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)

We have;

The coordinate of the highest point reached by the ball = (50, 125)

Therefore;

(h, k) = (50, 125)

Substituting the above values in the equation of the parabola gives;

y = a·(x - 50)² + 125

At x = 100, y = 0, which gives;

0 = a·(100 - 50)² + 125 = a·2500 + 125

0 = a·2500 + 125

a = -125/2500 = -0.05

Therefore, we have;

y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125

y  = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x

y =  -0.05·x² + 5·x

The equation that models the path of the ball is y =  -0.05·x² + 5·x.