SOLUTION: Flights of leaping animals typically have parabolic paths. The frog leaps on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet.

Question 523989: Flights of leaping animals typically have parabolic paths. The frog leaps on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet. Find a standard equation for the path of the frog. Assume a = 0.5.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Flights of leaping animals typically have parabolic paths. The frog leaps on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet. Find a standard equation for the path of the frog. Assume a = 0.5.
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Standard form of equation for parabola: y=A(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex, A being a multiplier which affects the steepness or slope of the curve.
Construct a parabola that opens downward as follows:
Place the vertex at the origin (0,0)
This makes the standard form: y=Ax^2
Two ends of the parabola meet the ground at (-9/2,-3/2)(left side) and (9/2,-3/2)(right side)
The problem is to find A
..
Using the coordinates of the point where the parabola meets the ground on the right side.
-3/2=A(9/2)^2
-3/2=A(81/4)
-12=162A
A=-12/162=-1/13.5
Equation: y=-x^2/13.5
see graph below as a visual check

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