SOLUTION: 9. Ticket Sales. The number of tickets sold each day for an upcoming performance of Handel’s Messiah is given by ,N(x) -0.4x^2+9x+11 where x is the number of days since the con

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 9. Ticket Sales. The number of tickets sold each day for an upcoming performance of Handel’s Messiah is given by ,N(x) -0.4x^2+9x+11 where x is the number of days since the con      Log On


   

Question 129801: 9. Ticket Sales. The number of tickets sold each day for
an upcoming performance of Handel’s Messiah is
given by
,N(x) -0.4x^2+9x+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 by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
N%28x%29+-.4x%5E2+%2B+9x+%2B+11
This is a parabola that peaks at the
midpoint of the 2 roots which are
found by applying the formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
I can decompose this into
x%5B1%5D+=+%28-b%29%2F%282a%29+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282a%29+
and
x%5B2%5D+=+%28-b%29%2F%282a%29+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282a%29+
The midpoint of these is -%28b%2F2a%29
The equation is in the form y+=+ax%5E2+%2B+bx+%2B+c
a+=+-.4
b+=+9
-%28b%2F2a%29+=+-%289%2F%282%2A%28-.4%29%29%29
-%28b%2F2a%29+=+9%2F.8
-%28b%2F2a%29+=+11.25
This is days after concert starts when the ticket sales peak
when N%28x%29
N%28x%29+-.4x%5E2+%2B+9x+%2B+11
N%2811.25%29+=+-.4%2A11.25%5E2+%2B+9%2A11.25+%2B+11
N%2811.25%29+=+-50.625+%2B+101.25+%2B+11
N%2811.25%29+=+61.625
This is the daily tickets sales peak
I'll plot the equation to check
+graph%28+600%2C+600%2C+-5%2C+26%2C+-5%2C+65%2C+-.4x%5E2+%2B+9x+%2B+11%29+