Question

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.. . Create an equation. Use the graph below to create the equation of the rainbow parabola.

Answer 1

y = a(x - p)(x - q)
p and q are the zeros of the parabola, -6 and 6 y = a(x + 6)(x - 6)

Substitute third point (0, 36) into the above equation to solve for a.

y = a(x + 6)(x - 6)

36 = a(0+6)(0-6)

36 = a(-36)

a = -1

So the equation is

y = -(x + 6)(x - 6)