Posted by **HUNU** on Monday, January 23, 2012 at 9:39pm.

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!

- Tough Math -
**Reiny**, Monday, January 23, 2012 at 10:40pm
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!

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