Problem preview

A-CED.2 Warmup M3-009-A09-V02

Create equations in two or more variables, graph them, and interpret relationships with labels and scales.

Find and interpret every intersection of competing model graphs

Problem

Graph $R(x)~=~-2x^2~+~40x$ and $y~=~150$ for quantity $x~\ge~0$. Find every intersection and interpret each in the revenue context.

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The x-intercepts (0, $0) and (20, $0) show that revenue reaches the $150 target at quantities 0 and 20.

Graph y=-2x²+40x and y=150 for x≥0. They intersect at (5, $150) and (15, $150), so modeled revenue reaches the $150 target at quantities 5 and 15.

The vertex (10, $200) is the target intersection, so revenue reaches $150 at quantity 10.

The symmetric points (5, $150), (10, $200), and (15, $150) are all target intersections.

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Curriculum context

Course: Math III
Standard: A-CED.2
Category: Algebra
Domain: Creating Equations
Objective: Create equations in two or more variables, graph them, and interpret relationships with labels and scales.
Problem type: Find and interpret every intersection of competing model graphs