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M2-011-A13-V03
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A-SSE.3.a
Warmup
M2-011-A13-V03
Factor quadratics to reveal zeros of the function they define.
Interpret factors in an area expression
Problem
For the pictured rectangle with \(A=x(x+7)\), identify its side lengths and their difference, including units. Derive the positive-length domain and explain the contextual status of both algebraic zeros.
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A
The side lengths are x and x + 7, but only x + 7 needs to be positive. Both physical lengths must be positive.
B
Negative or zero side lengths are valid rectangles, so 0 and −7 are valid physical dimensions. A positive-area rectangle requires positive lengths.
C
The side lengths are x and x + 7 units, so the area is in square units. A positive-area rectangle requires x > 0; 0 and −7 are algebraic zero boundaries, and 0 is the degenerate boundary.
D
The factors are square-unit areas, so their product has fourth-power units and x may be any real number. The factors represent lengths here.
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Curriculum context
Standard A-SSE.3.a
Category Algebra
Domain Seeing Structure in Expressions
Objective Factor quadratics to reveal zeros of the function they define.
Problem type Interpret factors in an area expression
