Given:
Given that the points
[tex](x,y)=(0,11)[/tex]And vertex
[tex](h,k)=(3,-7)[/tex]Required:
To find the equation of the parabola.
Explanation:
The equation of parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex]Therefore,
[tex]y=a(x-3)^2-7[/tex]Now we have to find a, by using the points.
[tex]\begin{gathered} 11=a(0-3)^2-7 \\ \\ 11=9a-7 \\ \\ 11+7=9a \\ \\ 9a=18 \\ \\ a=\frac{18}{9} \\ \\ a=2 \end{gathered}[/tex]So,
[tex]y=2(x-3)^2-7[/tex]Final Answer:
[tex]y=2(x-3)^2-7[/tex]