y = a (x - 2)^2 + 13............vertex form y= a(x - h)^2 + k...with vertex (h, k)
5 = a(0 -2)^2 + 13
5= 4a + 13
- 8 = 4a
-2 = a
y = -2 (x - 2)^2 + 13........now let y=0 and find the x intercept
0 = -2(x - 2)^2 + 13...........subtract 13
-13= -2(x - 2)^2................divide by -2
-13/-2 = (x - 2)^2.............simplify
13/2 = (x - 2)^2............take the sq rts.
√(13/2) = x - 2..............√6.5 =2.55........add 2
x = 4.55