Problema Solution
Sasha is training her dog bingo to run across an arched ramp which is the shape of a parabola.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 horizontal distance of 2 feet from the 1st treat and bingo is 6 feet above the ground when he reaches the top of the ramp. Write a function to represent bingo's height above the ground as he walks across the ramp in terms of his distance from the beginning of the ramp
Answer provided by our tutors
we need to find parabolic function
f(x) = ax^2 + bx + c,
where f(x) is Bingo's height above the ground, x the horizontal distance from the start position
we know that in the start position x = 0 and f(x) = 0 thus
a*0^2 + b*0 + c = 0 => c = 0
for x = 2 we know that f(2) = 6
a*2^2 + b*2 = 6
4a + 2b = 6 divide both sides by 2
2a + b = 3
we also know that for x = 2 f(2) = 6 is the maximum of the function
6 = c - b^2/(4a)
6 = 0 - b^2/(4a)
b^2 = - 24a
a = - b^2/24 plug into 2a + b = 3
-2*(b^2/24) + b = 3
by solving we find
b = 6
click here to see the step by step solution of the quadratic equation
a = -36/24 = - 3/2
f(x) = -(3/2)x^2 + 6x is the function that represents Bingo's height
if we draw the graph of the function we will see that indeed it describes the movement of Bingo
see the graph of the function by clicking here