Hi,
P(x) = –x^2 + 110x – 1,000 || yes, P(5)= -475
P(x) = -(x-55)^2 + 55^2 - 1000
P(x) = -(x-55)^2 + 2025 ||Parabola opening downward V(55,2025)
0 = -(x-55)^2 + 2025
(x-55)^2 = 2025
x = 55 ± 45, x-intercepts are 10 and 100
sketching: important to get in your Vertex and x-intercepts