Tough Math
posted by HUNU on .
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(xz1)(xz2) where z1 and z2 are the zeros (or roots) of the quadratic polynomial (or xintercepts of the graph) and C is a scaling constant that needs to be determined.
Thanks!

I guess we are assuming that the path will be a parabola
make the following sketch
on the xaxis, 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 = 432214.26 = 217.74
then OA = 217.74214.26 = 3.48 OC = 432+3.48 = 435.48
so parabola =
y = C(x0)(x435.48)
but (217.74 , 102.51) lies on it (the vertex)
102.74 = C(217.74)(217.74)
C = .00216
y = .00216x(x435.48)
check:
if x = 3.48 , the height should be 3.24 ft
y = .00216(3.48)(432)
= 3.247 YEAHHHH!