Question

A basketball player stands near the middle of the court and throws the ball toward the basket.

Answer 1

Answer:

A function to represent the height of the ball in terms of its distance from the player's hands is $y=\frac{-1}{54}(x-18)^2+12$

Step-by-step explanation:

General equation of parabola in vertex form $y= a(x-h)^2+k$

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

$y=a(x-18)^2+12$  ---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,$6=a(0-18)^2+12$

6=324a+12

-6=324a

$\frac{-6}{324}=a$

$\frac{-1}{54}=a$

Substitute the value in 1

So,$y=\frac{-1}{54}(x-18)^2+12$

Hence a function to represent the height of the ball in terms of its distance from the player's hands is $y=\frac{-1}{54}(x-18)^2+12$