Question 50100
P(x)= -x^2+40x+825
Rewrite as follows:

P(x)-825 = -(x^2-40x)
Complete the square as follows:

P(x)-825-400 = -(x^2-40x+400)
P(x)-1225 = -(x-20)^2
This follows the form 4p(y-k)=-(x-h)^2
where (h,k) is the vertex.
The vertex is (20,1225)
The P(x) intercept is (0,825)
The x-intercepts are:
x=[-40+-sqrt(40^2+4(825)]/-2
x=[-40+-70]/-2
x=(55,0), (-15,0)

Cheers,
Stan H.