Question 1085857

find the x-intercepts of the parabola with vertex (-3,16) and y-intercept (0,-20). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth
<pre>{{{y = a(x - h)^2 + k}}} <===== Vertex form of a parabolic equation
{{{- 20 = a(0 - - 3)2 + 16}}} ------- Substituting (0, - 20) for (x, y) and (- 3, 16) for (h, k)
- 20 = 9a + 16
- 20 - 16 = 9a
- 36 = 9a
{{{matrix(1,5, (- 36)/9, "=", a, "=", - 4)}}}

{{{y = a(x - h)^2 + k}}} <===== Vertex form of a parabolic equation
{{{0 = - 4(x - - 3)^2 + 16}}} ------- Substituting 0 for y,  - 4 for a, and (- 3, 16) for (h, k)
{{{0 = - 4(x + 3)^2 + 16}}}
{{{0 = - 4(x^2 + 6x + 9) + 16}}}
{{{0 = - 4x^2 - 24x - 36 + 16}}}
{{{0 = - 4x^2 - 24x - 20}}}
{{{- 4(0) = - 4(x^2 + 6x + 5)}}}
{{{x^2 + 6x + 5 = 0}}}
(x + 5)(x + 1) = 0
x = - 5		OR    		 x = - 1
{{{highlight_green(matrix(2,4, x-intercept[1], "=", "(- 5,", "0)", x-intercept[2], "=", "(- 1,", "0)"))}}}</pre>