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.

Answer 1

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.