Math Problem Statement

A company sells baseball necklaces at several tournaments. The amount of profit, f(x), is related to the selling price of each necklace, x, is modeled by the function below.

f(x)=−9x2f(x)=−9x2

+465x−3060+465x−3060

Find the price the necklaces should be sold to make the maximum profit.

The necklaces should be sold for $2946.25 to make the maximum profit.

The necklaces should be sold for $43.92 to make the maximum profit.

The necklaces should be sold for $25.83 to make the maximum profit.

The necklaces should be sold for $7.74 to make the maximum profit.

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Solution

To find the price at which the necklaces should be sold to make the maximum profit, we need to determine the vertex of the quadratic function. The function is given by:

f(x)=−9x2+465x−3060f(x) = -9x^2 + 465x - 3060

For a quadratic function in the form f(x)=ax2+bx+cf(x) = ax^2 + bx + c, the x-coordinate of the vertex (which gives the price that maximizes the profit) is given by the formula:

x=−b2ax = \frac{-b}{2a}

Here, a=−9a = -9, b=465b = 465, and c=−3060c = -3060. Plug

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Vertex of a Parabola

Formulas

Vertex formula x = -b / 2a

Theorems

Quadratic function vertex theorem

Suitable Grade Level

Grades 9-11

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