Tough Math
posted by HUNU .
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!
Respond to this Question
Similar Questions

algebra
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.  … 
precalc
Physics: a ball is thrown vertically upward with an initial velocity of 80 feet per second. the distance (in feet) of the ball from the ground after t seconds if s=80t16tt^2 a) draw the illustration b) for what time interval is the … 
Math
Can you please help me with a math problem 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 … 
math
a baseball is hit with an initial velocity of 75 feet per second from the height of 3 feet. The function h(t)=16t squared + 75t + 3 models the path of the baseball where t represents the time in seconds that the ball has been traveling … 
Math
A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t)=96t16t^2 a.) at what time will the ball strike the ground b.) for what … 
PreCalculus
A ball is thrown vertically upward with an initial velocity of 64 feet per second. The distance(in feet) of the ball from the ground after t seconds is s=64t16t. At what time will the ball strike the ground? 
calculus
I need help with this problem: The path traveled by a golf ball with a 9iron can be modeled with the quadratic equation, y= 0.042xsquared + 5x, where x is the distance in yards from the point it was hit and y is the height of the … 
math
A robotic basketball player tosses a ball upward from a height of 7 feet, at an initial speed of 111 feet per second. The height of the ball is modeled by the equation: h=−16t2+111t+7, where h is the height above the ground in … 
Precalculos
A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is S(t)=96t16t^2. At what time t will the ball strike the ground? 
Math
Using his driver on the 7th tee, Chris hits an excellent shot, right down the middle of the fairway. The ball follows the parabolic path shown in the figure, described by the quadratic function: h(x)=0.5x0.002x^2. This relates the …