Question 638113
The equation of parabola with vertex (h,k) is {{{y = a(x-h)^2 + k}}}.
Therefore, the equation of the parabola with vertex (4,75) is {{{y = a(x-4)^2 + 75}}}. When x = 0, y = 16a + 75. 
So 16a + 75 = 27 and a = -3.
The equation of parabola is {{{y = -3(x - 4)^2 + 75}}}.
To solve the x-intercepts, let y = 0 and solve for x:
 {{{ -3(x - 4)^2 + 75 = 0}}}
 {{{ -3(x - 4)^2 = -75}}}
 {{{(x - 4)^2 = 25}}}
 {{{x - 4 = 5}}} or {{{x - 4 = -5}}}
 {{{x = 9}}} or {{{x = -1}}}
Answer: (9,0),(-1,0)