Math/Algebra

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The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)= -0.4x^2 + 8.8x +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?

Ticket sales will peak ___ days after the concert was first announced.

The number of tickets sold on that day will be ____. (Round to the nearest integer)

  • Math/Algebra -

    find the roots to the quadratic. Maximum will be halfway between the roots.

  • Math/Algebra -

    That's where I got lost was when I was trying to find the roots of the quadratic equation. I guess I just need more practice with these roots.

  • Math/Algebra -

    0.4 x 0.4 = 0.16
    8.8 x 8.8 = 77.44
    15 x 15 = 225

  • Math/Algebra -

    to find the roots of -0.4x^2 + 8.8x +15 = 0
    I would first "clean-up" the equation. I don't like decimals in my equations so I would multiply each term by 10
    -4x^2 + 88x + 150 = 0
    divide by -2
    2x^2 - 44x - 75 = 0
    a=2, b=-44, c=-75
    x = (-b ± √(b^2 - 4ac))/(2a)
    = (44 ± √2536)/4
    = 23.5897 and -1.58987

    the halfway value of x, as bobpursely suggested, is 11
    so N(11) = -.4(121) + 8.8(11) + 15 = 63.4

    another way is to know that for any function
    f(x) = ax^2 + bx + c, the max/min occurs when
    x = -b/(2a)

    then -b/(2a) = -8.8/(2(-.4)) = 11 as above

  • Math/Algebra -

    So then I would end up with the ticket sales would peak 11 days after, and the number of tickets sold that day would be 63.4 Correct or No?

  • Math/Algebra -

    Although it says to round to the nearest integer. So this would actually be sales peak 11 days after, and the number of tickets sold would just be 63.

  • Math/Algebra -

    correct

  • Math/Algebra -

    Ahhhh Thank you very much! I seem to get lost when it comes to the cleaning up the decimals & then trying to get the square root if it is in decimal form. I appreciate your help Reiny :)!

  • Math/Algebra -

    The number of tickets sold each day for an upcoming Handel’s Messiah is given by N(x)=-0.5x^2+12x+15

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