Question

Suppose the ball was 3.24 feet above ground when it was hit, and that it reached a maximum height of approximately 102.51 feet when it had traveled a ground distance of approximately 214.26 feet. The ball lands after traveling a ground distance of approximately 432 feet.

Find an equation of the form y = C(x-z1)(x-z2) where z1 and z2 are the zeros (or roots) of the quadratic polynomial (or x-intercepts of the graph) and C is a scaling constant that needs to be determined.

Thanks!

Answer 1

I guess we are assuming that the path will be a parabola

make the following sketch
on the x-axis, label 3 points A, B , and C
where A is where the ball is hit,
B is the maximum point, and
C is the place where the Ball hits the ground
sketch the parabola, and continue it to the left of A to hit the origin at O

so C is (217,74)
AB = 214.26
but B must be the midpoint of OC
so BC = 432-214.26 = 217.74
then OA = 217.74-214.26 = 3.48 OC = 432+3.48 = 435.48
so parabola =
y = C(x-0)(x-435.48)
but (217.74 , 102.51) lies on it (the vertex)
102.74 = C(217.74)(-217.74)
C = -.00216

y = -.00216x(x-435.48)

check:
if x = 3.48 , the height should be 3.24 ft
y = -.00216(3.48)(-432)
= 3.247 YEAHHHH!