SOLUTION: The number of tickets sold each day for an upcoming performance of​ Handel's Messiah is given by Upper N left parenthesis x right parenthesis equals negative 0.6 x squared pl

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The number of tickets sold each day for an upcoming performance of​ Handel's Messiah is given by Upper N left parenthesis x right parenthesis equals negative 0.6 x squared pl      Log On


   

Question 1121157: The number of tickets sold each day for an upcoming performance of​ Handel's Messiah is given by Upper N left parenthesis x right parenthesis equals negative 0.6 x squared plus 14.4 x plus 14​, 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 Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula looks like:

N(x) = -.6x^2 + 14.4x + 14

N is the function name.
x is the argument of the function.
the expression on the right is the formula of the function.

you could replace N(x) with y and the function would read:

y = -.6x^2 + 14.4x + 14

you can graph the equation in this form.

the graph would look like this:

$$$

you can see from the graph that the maximum value of y (also called N(x)) is 100.4 when x = 12.

this can also be found by formula.

the formula is x = -b/2a.

the equation has to be in standard form of y = ax^2 + bx + c.

it's already in that form.

y = -.6x^2 + 14.4x + 14 gets you:

a = -.6
b = 14.4
c = 14

x = -b/2a gets you x = 14.4 / -1.2

this results in x = 12.

when x = 12, the function of y = -.6x^2 + 14.4x + 14 becomes y = -.6 * 12^2 + 14.4 * 12 + 14 which becomes y = 100.4

when x is 12, y is 100.4

x represents the number of days since the concert was first announced.

y represents the number of tickets sold each day.

here's a reference on functional notation.

https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html

here's another reference on functional notation.

https://www.purplemath.com/modules/fcnnot.htm

here's a reference on quadratic equations.

https://www.cliffsnotes.com/study-guides/algebra/algebra-i/quadratic-equations/solving-quadratic-equations

lots more on how to solve quadratic equations from purplemath.

https://www.google.com/search?q=quadratic+equations+purplemath&oq=quadratic+equations+purplemath&aqs=chrome.0.69i59j69i60j0l4.7671j1j7&sourceid=chrome&ie=UTF-8