write a quadratic function to represent each situtation using the given information

Question

Sasha is training her dog, Bingo, to run across an arched ramp, which is the shape of a proabla, To help Bingo get across the ramp, Sasha places a treat on the ground where the arched ramp begins and one at the top of the ramp. The treat at the top of the ramp is a horizonal distance of 2 feet from the first treat, and bingo is 6 feet above the ground when he reaches the top of the ramp. Write a function to represent Bingos hight above the ground as he walks across the ramp in terms of distance from the beginning of the ramp

Answer 1

h-k=a(x-b)^2 is a quadratic form where x is horizontal distance and h height above the ground. The maximum height is 6' when x=2', so b=2 and k=6: h-6=a(x-2)^2. When x=0, h=0, -6=4a, a=-3/2. h=6-(3/2)(x-2)^2. Note that when x=4, h=0. The function is valid for 0<x<4, because h>0.