Algebra-2

First, we know that the x-coordinate of the vertex of a parabola given in factored form is the average of the two roots (i.e., the x-intercepts).

So, if the vertex is at (-2, 16), then (-2) is the average of p and q.

That means (p + q)/2 = -2, which simplifies to p + q = -4.

Next, since the graph passes through (0, -12), when x = 0, g(x) = -12.

Substituting these values into g...