The vertex form of a parabola is given by $y = a(x-h)^2 + k$, where $(h,k)$ is the vertex. In this case, we are given that the vertex is $(-4,7)$. So, our equation can be written as $y = a(x-(-4))^2 + 7$. Simplifying this expression gives $y = a(x+4)^2 + 7$. To find the value of $a$, we can use the fact that the parabola passes through the point $(-3,8)$. Plugging in these values into the equation, we get $8 = a((-3)+4)^2 + 7$. Simplifying this equation gives us $8 = a(1)^2 + 7$. Solving for $a$, we have $8 = a + 7$, so $a=1$. Therefore, the equation of the parabola in vertex form is $y = (x+4)^2 + 7$.
