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Interpreting Quadratic Functions in Factored Form

Interpreting Quadratic Functions in Factored Form 1.18 - Solution

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To match the given function with its graph, we will find its zeros. To do so, we will rewrite it a little bit. y=14(x+5)(x3)    y=14(x(-5))(x3)\begin{gathered} y=\dfrac{1}{4}(x+5)(x-3) \ \ \Leftrightarrow \ \ y=\dfrac{1}{4}(x-(\text{-} 5))(x-3) \end{gathered} Note that now the quadratic function is written in factored form. Factored form: y=a(xp)(xq)Given equation: y=14(x(-5))(x3)\begin{aligned} \textbf{Factored form:}&\ y={\color{#0000FF}{a}}(x-{\color{#009600}{p}})(x-{\color{#FF0000}{q}}) \\ \textbf{Given equation:}&\ y={\color{#0000FF}{\dfrac{1}{4}}}(x-({\color{#009600}{\text{-} 5}}))(x-{\color{#FF0000}{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}{3}}. This matches choice V.