A rectangle has sides \(x\) and \(x+6\) with \(x\ge~0\), so \(A(x)=x(x+6)\). Find both algebraic \(x\text{-}\text{intercepts}\), filter them using the side-length domain, and explain what the retained \(\text{zero}\text{-}\text{area}\) boundary represents physically.

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At x=0, the rectangle has positive area.

The x-intercepts are area outputs 0 and −6 square units.

Both x=0 and x=−6 are valid side lengths where the rectangle has area 0.

The algebraic roots are x=0 and x=−6, but only x=0 is a valid side length; it gives a degenerate rectangle with area 0.

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Curriculum context

Course: Math II
Standard: F-IF.4
Category: Functions
Domain: Interpreting Functions
Objective: Interpret key graph/table features of quadratic models in context.
Problem type: Interpret the x-intercepts of a quadratic model in context