Math Problem Statement

the owner of a video game store has determined that the profits P of the store are approximately given by P(x)=-x^2+130x+70 where x is the number of videos rented daily find the maximum profit to the nearest dollar

Solution

The given profit function is P(x)=x2+130x+70P(x) = -x^2 + 130x + 70, which represents a downward-opening parabola. The maximum profit will occur at the vertex of the parabola.

Formula for the vertex

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex of a Parabola

Formulas

Vertex formula: x = -b/(2a)
Standard form of a quadratic equation: ax^2 + bx + c

Theorems

Vertex Theorem for Quadratic Functions

Suitable Grade Level

Grades 9-10