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Rockin' Jon, a music club owner, is planning for the next annual Rockin' Jon's New Year's Eve Jamfest. He has noticed that when he charges more for tickets for the show, fewer people buy tickets. Rockin' Jon's total revenue from selling tickets for the Jamfest, in dollars, can be modeled by the expression p(576−16p)p(576 - 16p), where pp is the price per ticket in dollars. This expression can be written in factored form as −16p(p−36)-16p(p - 36).\newlineWhat does the number 3636 represent in the expression?\newline(A) Rockin' Jon's minimum total revenue in dollars\newline(B) the price per Jamfest ticket in dollars so that Rockin' Jon's total revenue is zero\newline(C) Rockin' Jon's maximum total revenue in dollars\newline(D) the price per Jamfest ticket in dollars that maximizes Rockin' Jon's total revenue

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Q. Rockin' Jon, a music club owner, is planning for the next annual Rockin' Jon's New Year's Eve Jamfest. He has noticed that when he charges more for tickets for the show, fewer people buy tickets. Rockin' Jon's total revenue from selling tickets for the Jamfest, in dollars, can be modeled by the expression p(576−16p)p(576 - 16p), where pp is the price per ticket in dollars. This expression can be written in factored form as −16p(p−36)-16p(p - 36).\newlineWhat does the number 3636 represent in the expression?\newline(A) Rockin' Jon's minimum total revenue in dollars\newline(B) the price per Jamfest ticket in dollars so that Rockin' Jon's total revenue is zero\newline(C) Rockin' Jon's maximum total revenue in dollars\newline(D) the price per Jamfest ticket in dollars that maximizes Rockin' Jon's total revenue
  1. Rewrite Expression: Rewrite the expression in factored form: −16p(p−36)-16p(p - 36).
  2. Identify Zero: Identify the zero of the quadratic function: Set −16p(p−36)=0-16p(p - 36) = 0 and solve for pp.
  3. Solve Equation: Solve the equation: −16p=0-16p = 0 or p−36=0p - 36 = 0.
  4. Find Value of p: Find the value of pp when the revenue is zero: p=0p = 0 or p=36p = 36.
  5. Interpret p=36p = 36: Interpret the value p=36p = 36: This is the price per ticket that makes the revenue zero, which means it's the maximum price before the revenue starts decreasing.

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