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Interpreting Quadratic Functions in Factored Form

Interpreting Quadratic Functions in Factored Form 1.17 - Solution

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To match the given function with its graph, we will find its zeros. To do so, we need to rewrite it. y=(x+5)(x+3)    y=1(x(-5))(x(-3))\begin{gathered} y=(x+5)(x+3) \ \ \Leftrightarrow \ \ y=1(x-(\text{-} 5))(x-(\text{-} 3)) \end{gathered} Note that now the quadratic function is written in factored form. Factored form: y=a(xp)(xq)Given equation: y=1(x(-5))(x(-3))\begin{aligned} \textbf{Factored form:}&\ y={\color{#0000FF}{a}}(x-{\color{#009600}{p}})(x-{\color{#FF0000}{q}}) \\ \textbf{Given equation:}&\ y={\color{#0000FF}{1}}(x-({\color{#009600}{\text{-} 5}}))(x-({\color{#FF0000}{\text{-} 3}})) \end{aligned} In this form, the zeros of the function are p{\color{#009600}{p}} and q.{\color{#FF0000}{q}}. Therefore, the zeros of the given function are -5{\color{#009600}{\text{-} 5}} and -3.{\color{#FF0000}{\text{-} 3}}. This matches choice III.