Problem

A straight path is \(y=x+3\) and a curved path is \(y=x^{2}+3\). Equate and simplify the models, retain the \(\text{zero}\) solution, calculate both \(y\)-coordinates, interpret the intersections, and check the displayed answer graph.

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System: y = x + 3 and y = x² + 3. Set equal: x + 3 = x² + 3, so x² − x = 0 = x(x − 1). Inputs 0 and 1 give points (0, 3) and (1, 4).

System: y = x + 3 and y = x² + 3. Set equal: x + 3 = x² − 3, so x² − x − 6 = 0. Inputs −2 and 3 give points (−2, 1) and (3, 6): these are claimed intersections.

System: y = x + 3 and y = x² + 3. Set equal: x + 3 = x² + 3, so x² − x = 0. Input 1 gives point (1, 4): the zero input is omitted.

System: y = x + 3 and y = x² + 3. Set equal: x + 3 = x² + 3, so x² − x = 0. Inputs 0 and 1 give points (0, 0) and (1, 1): the y-values are omitted.

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A straight path is \(y=x+3\) and a curved path is \(y=x^{2}+3\). Equate and simplify the models, retain the \(\text{zero}\) solution, calculate both \(y\)-coordinates, interpret the intersections, and check the displayed answer graph.

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