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M2-003-A11-V03
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A-CED.2
Warmup
M2-003-A11-V03
Create equations in two or more variables and graph them with appropriate labels and scales.
Write an equation from a table and describe the graph features
Problem
Analyze the pattern in the displayed table. Use first and second differences to classify the relationship, write its equation, and describe the graph's vertex, opening, and direction over the listed inputs.
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A
The first differences are 3, 5, and 7, with constant second differences of 2, so the pattern is quadratic. Its equation is y=(x+1)² with vertex (−1,0); the graph opens downward and decreases.
B
The first differences are 3, 5, and 7, so the pattern is linear. It starts at 1 with slope 3: y=3x+1. Its graph is an increasing line.
C
The first differences are 3, 5, and 7, with constant second differences of 2, so the pattern is quadratic. Its equation is y=(x−1)² with vertex (1,0); the graph opens upward.
D
The first differences are 3, 5, and 7, with constant second differences of 2, so the pattern is quadratic. Its equation is y=(x+1)² with vertex (−1,0); the graph opens upward and increases for the listed x-values.
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Curriculum context
Standard A-CED.2
Category Algebra
Domain Creating Equations
Objective Create equations in two or more variables and graph them with appropriate labels and scales.
Problem type Write an equation from a table and describe the graph features
