Answer:
A function to represent the height of the ball in terms of its distance from the player's hands is [tex]y=\frac{-1}{54}(x-18)^2+12[/tex]
Step-by-step explanation:
General equation of parabola in vertex form [tex]y= a(x-h)^2+k[/tex]
y represents the height
x represents horizontal distance
(h,k) is the coordinates of vertex of parabola
We are given that The ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.
So,(h,k)=(18,12)
Substitute the value in equation
[tex]y=a(x-18)^2+12[/tex] ---1
The ball leaves the player's hands at a height of 6 feet above the ground and the distance at this time is 0
So, y = 6
So,[tex]6=a(0-18)^2+12[/tex]
6=324a+12
-6=324a
[tex]\frac{-6}{324}=a[/tex]
[tex]\frac{-1}{54}=a[/tex]
Substitute the value in 1
So,[tex]y=\frac{-1}{54}(x-18)^2+12[/tex]
Hence a function to represent the height of the ball in terms of its distance from the player's hands is [tex]y=\frac{-1}{54}(x-18)^2+12[/tex]
