Find the x intercept of the parabola with vertex (2 13) and y intercept (0 5)

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