Question 1128838

A quadratic function has a minimum of -8 and an x-intercept of -5. Its axis of symmetry is x=-3. Find the y-intercept of this quadratic function.
<pre>Vertex form of a parabola: {{{matrix(1,3, y, "=", a(x - h)^2 + k)}}}
{{{matrix(1,3, 0, "=", a(- 5 - - 3)^2 - 8)}}} ------- Substituting (- 3, - 8) for (h, k), and (- 5, 0) for (x, y)
0 = 4a - 8
8 = 4a
{{{matrix(1,5, a, "=", 8/4, "=", 2)}}}
We now get: {{{matrix(1,3, y, "=", 2(x + 3)^2 - 8)}}}
{{{matrix(1,3, y, "=", 2(0 + 3)^2 - 8)}}} ------- Substituting 0 for x
{{{highlight_green(matrix(1,4, "y-intercept:", 2(9) - 8, "=", 10))}}}