Question

Find the equation of the parabola that has zeros of x = - 6 and x = 6 and a yintercept of (0, 4) .

Answer 1

Since the zeros are symmetrical to the y axis, the equation can be written as
y=a(x-b)(x+b), where a is a scale factor and b is x intercept. By plugging in the zeros, you get y=A(x-6)(x+6). Now we can plug in the (0,4) and solve for a to get the scale factor.

4=A(0-6)(0+6)
4=A(-36)
-36A=4
A=-1/9

Therefore the equation is Y=-1/9(x-6)(x+6), or Y=-1/9(x^2-36)

Hope this helps!