Question

Below is the graph of a parabola with its vertex and another point on the parabola labeled.Write an equation of the parabola.(-2,4).(1, -2)

Answer 1

The vertex form of a parabola is given by:

`x=a(y-k)^2+h`

Where the vertex is:

`\begin{gathered} V(h,k)=(-2,4) \\ so\colon \\ x=a(y-4)^2-2 \\ x=a(y-4)^2-2 \end{gathered}`

for (1,-2):

`\begin{gathered} 1=a(-2-4)^2-2 \\ 1=a(-6)^2-2 \\ 1=36a-2 \\ solve_{\text{ }}for_{\text{ }}a\colon \\ 36a=1+2 \\ 36a=3 \\ a=(3)/(36) \\ a=(1)/(12) \\ \end{gathered}`

therefore:

`x=(1)/(12)(y-4)^2-2`