Question

Suppose the ball was 2.74 feet above ground when it was hit. It reached a max. height of 116.3ft when it was approx 215.3 ft away from where he hit the ball. The ball lands after travelling a ground distance of approx 433.1 ft.

-- find an equation in form of y=C(x-z1)(x-z2) where z1 and z2 are the roots and C is scaling constant.

-- find the scaling constant C.

Answer 1

Since the vertex is halfway between z1 and z2

215.3 = (z1+z2)/2
But, we know that z2=433.1
so, z1 = -2.5

Now we have y = C(x+2.5)(x-433.1)
and since y(215.3) = 116.3

116.3 = C217.8^2
C = 0.00245(x+2.5)(x-433.1)

Better double-check my math, but it seems good to me.