Kevin writes and self-publishes his own quarterly sports magazine, The Fresh Catch. He has found that when he charges more per issue, he sells fewer issues overall that quarter. His revenue from selling the issues, in dollars, can be modeled by the expression $p(9,000 - 1,500p)$ , where $p$ is the price per issue in dollars. This expression can be written in factored form as $-1,500p(p - 6)$ . $\newline$ What does the number $6$ represent in the expression? $\newline$ (A)the price per issue in dollars that maximizes Kevin's revenue $\newline$ (B)the price per issue in dollars so that Kevin's revenue is zero $\newline$ (C)Kevin's maximum revenue in dollars $\newline$ (D)Kevin's minimum revenue in dollars

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Algebra 2

Interpret parts of quadratic expressions: word problems

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Q. Kevin writes and self-publishes his own quarterly sports magazine, The Fresh Catch. He has found that when he charges more per issue, he sells fewer issues overall that quarter. His revenue from selling the issues, in dollars, can be modeled by the expression

p(9,000 - 1,500p)

, where

p

is the price per issue in dollars. This expression can be written in factored form as

-1,500p(p - 6)

\newline

What does the number

6

represent in the expression?

\newline

(A)the price per issue in dollars that maximizes Kevin's revenue

\newline

(B)the price per issue in dollars so that Kevin's revenue is zero

\newline

(C)Kevin's maximum revenue in dollars

\newline

(D)Kevin's minimum revenue in dollars

Rewrite expression: Rewrite the expression in factored form: $-1,500p(p - 6)$ .
Identify zero points: Identify the zero points of the revenue function by setting the factored form equal to zero: $-1,500p(p - 6) = 0$ .
Solve for $p$ : Solve for $p$ : $p = 0$ or $p - 6 = 0$ , which gives $p = 6$ .
Interpret zero points: Interpret the zero points: $p = 0$ means Kevin sells the magazine for $\$0$ , which would result in no revenue. $p = 6$ means that if Kevin charges $\$6$ per issue, the revenue will be zero because it's the point where the quantity sold drops to zero.
Conclude significance of $6$ : Conclude what the number $6$ represents: Since $p = 6$ is the price at which revenue drops to zero, it is the price per issue in dollars that maximizes Kevin's revenue before it starts to decrease again.