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

Y = a (x - 2)^2 + 13vertex 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 + 13now let y=0 and find the x intercept 

0 = -2(x - 2)^2 + 13subtract 13 

-13= -2(x - 2)^2divide by -2 

-13/-2 = (x - 2)^2simplify 

13/2 = (x - 2)^2take the sq rts. 

√(13/2) = x - 2√6.5 =2.55add 2 

x = 4.55

Are you trying to figure out the volume?