The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+12x+10, 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?
N(x)=-.4( x^2 -30 x -25)
N(x)=-.4( x^2-30x+225-250)
N(x)=-.4( x-15)^2 +.4(250)
so the maximum is at x=15
You solve for N(15).
Also, I recommend you graph this on your graphing calc, to see if it is correct.
To find when daily ticket sales will peak and how many tickets will be sold that day, we need to find the maximum value of the function N(x)=-0.4x^2+12x+10.
The maximum or minimum value of a quadratic function can be found using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, a = -0.4 and b = 12. Plugging these values into the formula, we get:
x = -(12) / (2 * -0.4)
x = -30 / -0.8
x = 37.5
So, the x-coordinate for the maximum point is x = 37.5.
Now that we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate or number of tickets sold:
N(37.5) = -0.4(37.5)^2 + 12(37.5) + 10
N(37.5) = -0.4(1406.25) + 450 + 10
N(37.5) = -562.5 + 450 + 10
N(37.5) = -102.5
Therefore, the daily ticket sales will peak after approximately 37.5 days since the concert was first announced, and the number of tickets sold that day will be -102.5 (which suggests a decrease in ticket sales on that day).