quadratic function with maximum and minimum

Question

the number of inmates in custody in us prisons and jails can be modeled by the quadratic function p(x)=-x^2+94x+1125 where p(x) is the number of inamtes and x is the number of years after 1990. in what year the number of inmates reach its maximum?what is the maximum number of inmates?

Answer 1

the maximum for such a function, a parabola opening downwardly, occurs at the vertex.

the x value of the vertex is -b/(2a) where a is the leading coefficient, -1, and b is 94.

Then the maximum number of inmates is p(x.for.vertex).