SOLUTION: The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.4x^2+12x+15 where x is the number of days since the concert was first announc

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Question 482759: The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.4x^2+12x+15 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 by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When a quadratic has the general form
+f%28x%29+=++ax%5E2+%2B+bx+%2B+c++, the peak is at x+=++-b%2F%282a%29+.
when +a+ is a negative number.
given:
+N%28x%29=+-.4x%5E2%2B12x%2B15+
xmax = -b%2F%282a%29+
+-b%2F%282a%29+=+-12%2F%282%2A%28-.4%29%29+
+-b%2F%282a%29+=+12%2F.8+
+-b%2F%282a%29+=+15+
daily ticket sales will peak 15 days after concert was announced
The number of tickets sold on that day will be
+N%2815%29=+-.4%2A15%5E2%2B12%2A15%2B15+
+N%2815%29=+-90+%2B+180+%2B+15+
+N%2815%29+=+105+
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You can check this by making sure that both
+N%2814%29 and N%2816%29 are smaller than +105+