Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Write a quadratic area function from variable side lengths
Problem
A rectangle has width \(x\) and length \(x+7\). Build \(A(x)\) from width times length, give both factored and expanded quadratic forms, state the area units, and identify the \(x\text{-}\text{values}\) that make both dimensions positive.
Big Picture
What this problem is really about
Rectangle area comes from multiplying the two side expressions, which naturally creates a quadratic and square units. We’ll write the factored model from width and length, expand it for an equivalent form, then intersect the two strict positivity conditions to identify the physical domain.
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