We have been given that a parabola has vertex [tex](-8,-7)[/tex] and also passes through the point [tex](-7,-4)[/tex]. We are asked to write the equation of the parabola in vertex form.
We know that vertex form of parabola in format [tex]y=a(x-h)^2+k[/tex], with a vertex at point (h,k).
Let us write equation of parabola using our given information as:
[tex]y=a(x-(-8))^2-7[/tex]
[tex]y=a(x+8)^2-7[/tex]
Now we will substitute the coordinates of point [tex](-7,-4)[/tex] to solve for a as:
[tex]-4=a(-7+8)^2-7[/tex]
[tex]-4=a(1)^2-7[/tex]
[tex]-4+7=a-7+7[/tex]
[tex]3=a[/tex]
Therefore, our required equation would be [tex]y=3(x+8)^2-7[/tex].
