Question 448525
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Hi
Find the X-intercepts of a parabola with the vertex at (-3,16)
and the Y-intercept at  (0,-20)
Using the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex
  y = a(x+3)^2 +16
 -20 = a * 9 + 16
 -36 = 9a
  -4 = a
  y = -4(x+3)^2 +16
x-intercepts when y = 0
 -4(x+3)^2 = -16
   (x+3)^2 = 4
    x+3 = ± 2
    x = -3 ± 2   x = -5  and x = -1

{{{drawing(300,300,  -20,20,-20,20,  blue(line(-3,20,-3,-20))  , grid(1),
circle(-3, 16,0.6),
circle(-5, 0,0.6),
circle(-1, 0,0.6),
graph( 300, 300, -20,20,-20,20, 0 ,-4(x+3)^2 +16 ))}}}