SOLUTION: The number of tickects sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+12x+11, where x is the number of days since the concert was first anno

Question 472475: The number of tickects sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+12x+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?

^means raising to that power
Found 2 solutions by ewatrrr, monika_p:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
Note:the vertex form of a parabola, where(h,k) is the vertex
N(x)= -0.4x^2+12x+11
N(x)=-0.4[x^2 -30x]+11
N(x)=-0.4[(x-15)^2 -225]+11
N(x)=-0.4[(x-15)^2 -225]+11
N(x)=-0.4(x-15)^2 +101 V(15,101) a = -.4 a<0, Parabola opens downward
V(15,101)is the Maximum Point. ticket sales peak on the 15th day with 101 sold

Answer by monika_p(71) (Show Source): You can put this solution on YOUR website!
In this case vertex is the high point of the parabola (ticket sales peak) because coefficient a= -0.4 is a negative number and the parabola opens downward
To answer this question you have to find coordinates of the vertex of parabola N(x)= -0.4x^2+12x+11 where x is number of days and y = N(x) is number of tickets sold
The general form of quadratic equation is y= ax^2+bx+c
x-coordinate of vertex
y-coordinate of vertex where d= b^2-4*a*c
Substitute for a, b, and c and you should get answer that on 15th day x=15 they will sell the most tickets y=101
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