A parabola written in vertex form is
[tex]f(x)=a(x-h)^2+k[/tex]
The coordinates (h, k) represents the vertex.
Since the vertex of our problem is (-1, 9), our parabola equation will have the form
[tex]G(x)=a(x-(-1))^2+9=a(x+1)^2+9[/tex]
We know that the point (-5, 4) belongs to this parabola. If we evaluate this point on our equation we can determinate the coefficient a.
[tex]\begin{gathered} 4=a(-5+1)^2+9 \\ 4-9=a(-4)^2+9-9 \\ -5=16a \\ 16a=-5 \\ a=-\frac{5}{16} \end{gathered}[/tex]
Then, our equation is
[tex]G(x)=-\frac{5}{16}(x-(-1))^2+9[/tex]
