SOLUTION: THE NUMBER OF TICKETS SOLD EACH DAY FOR AN UP COMING PERFORMANCE OF HANDLES IS GIVEN BY N(X)= -0.4X^2 +8.8X +15, WHERE X IS THE NUMBER OF DAYS SCINSE THE CONCERT WAS FIRST ANNOUNCE

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: THE NUMBER OF TICKETS SOLD EACH DAY FOR AN UP COMING PERFORMANCE OF HANDLES IS GIVEN BY N(X)= -0.4X^2 +8.8X +15, WHERE X IS THE NUMBER OF DAYS SCINSE THE CONCERT WAS FIRST ANNOUNCE      Log On


   

Question 371028: THE NUMBER OF TICKETS SOLD EACH DAY FOR AN UP COMING PERFORMANCE OF HANDLES IS GIVEN BY N(X)= -0.4X^2 +8.8X +15, WHERE X IS THE NUMBER OF DAYS SCINSE THE CONCERT WAS FIRST ANNOUNCED. WHEN WILL DAILY TICKET SALES PEAK? ALSO, HOW MANY TICKETS WILL BE SOLD THAT DAY?
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
N%28x%29=+-0.4x%5E2+%2B8.8x+%2B15
The easy way to solve this is based on understanding that the graph of N(x) is a parabola. And not only is it a parabola, it is a parabola that opens downward (because of the minus in front of the squared term and because the squared term is x (and not y)). Once we imagine a picture of a parabola that opens downward, we should realize that the maximum (highest) point will be the vertex of that parabola. So allwe have to do is figure out the vertex.

The quick way to find a vertex is to use x+=+%28-b%29%2F%282a%29 where the "a" and "b" come from the general equation of quadratic equations: y+=+ax%5E2+%2Bbx+%2Bc. Using this on N(x) we get:
x+=+%28-8.8%29%2F%282%2A%28-0.4%29%29+=+%28-8.8%29%2F%28-0.8%29+=+11
So 11 days after the announcement, the ticket sales will be at a peak. And N(11) will tell us how many tickets were sold on that day:
N%2811%29+=+-0.4%2811%29%5E2+%2B8.8%2811%29+%2B15
Simplifying...
N%2811%29+=+-0.4%28121%29+%2B8.8%2811%29+%2B15
N%2811%29+=+-48.4+%2B+96.8+%2B15
N%2811%29+=+63.4
So approximately 63 tickets were sold 11 days after the announcement of the concert.