The number of tickets sold each day for an up coming performance of Handel,s Messiah is given by N(x)=-0.4x^2+8x+11, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day.
So in effect you are finding the vertex of the downwards opening parabola
shortest way:
the x of the vertex is -b/(2a) = -8/-.8 = 10
when x = 10
N(10) = -.4(100) + 8(10)+11
= 51
The ticket sales will peak at day 10 and on that day 51 tickets are sold
method 2: complete the square
N(x) = -.4(x^2 + 8x + 11
= -.4(x^2 - 20x + 100 - 100) + 11
= -.4( (x-10)^2 - 100) + 11
= -.4(x-10)^2 + 51
read the answer off from that, same as my first way.
If you know Calculus, this is really trivial.