Hi
The average nightly attendance at a certain movie theater is
100 when the ticket price is $4.00.
The manager estimates that for each 10 cents reduction in price,
the average attendance will increase by 10
R(x) = 400 + (4-.10x)(100+10)
R(x) = -x^2 + 30x + 800 |Completing the square to put into the vertex form
the vertex form of a parabola,where(h,k) is the vertex
R(x) = -[(x-15)^2-625] + 800
R(x) = -(x-15)^2 + 1425 Vertex is (15,1425) it is a maximum point (a<0)
15*.10 = 1.50 reduction in ticket price.
Ticket = $4.00 - $1.50 = $2.50 and Revenue at that price is $1425