Question

Create an equation. Use the graph below to create the equation of the rainbow parabola.

Graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0.

Answer 1

The vertex form of a parabola:

`y=a(x-h)^2+k`
(h,k) - the coordiantes of the vertex

The vertex is (0,36).

`y=a(x-0)^2+36 \\ y=ax^2+36`

Now plug the coordinates (x,y) of one of the zeros into the equation and solve for a.

`0=a * 6^2+36 \\ 0=36a+36 \\ -36=36a \\ (-36)/(36)=a \\ a=-1 \\ \\ \boxed{y=-x^2+36}`