Step-by-step explanation:
The vertex form of a parabola can be written as
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) are the coordinates of the parabola's vertex. So our parabola has the equation
[tex]y = a(x + 7)^2 + 2[/tex]
Since the parabola passes through the point (-6, 4), we can solve for the constant a as follows:
[tex]4 = a(-6 + 7)^2 + 2 \Rightarrow a = 2[/tex]
Therefore, the vertex form of the equation for the parabola is
[tex]y = 2(x + 7)^2 +2[/tex]
