Answer:
The standard equation for a parabola in vertex form is:
y = a(x - h)^2 + k
where (h, k) are the coordinates of the vertex.
We know that the vertex of the parabola is (-5, -11), so we can plug these values into the equation to get:
y = a(x - (-5))^2 - 11
Simplifying this equation gives us:
y = a(x + 5)^2 - 11
Now, we need to find the value of "a". We do this by using the fact that the parabola passes through the point (-2, 16). So, we substitute these values for x and y in our equation to get:
16 = a(-2 + 5)^2 - 11
Simplifying this equation further gives us:
16 = 9a - 11
Add 11 to both sides:
27 = 9a
Divide both sides by 9:
a = 3
Substituting this value of "a" into our equation for y, we get:
y = 3(x + 5)^2 - 11
Therefore, the equation for the parabola with vertex (-5, -11) and passing through the point (-2, 16) is y = 3(x + 5)^2 - 11.