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Transformations of Quadratic Functions

Transformations of Quadratic Functions 1.11 - Solution

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We want to match the given function with its graph. We begin by noticing that the given function is a transformation of the form y=a(xh)2+k,y=a(x-{\color{#0000FF}{h}})^2+{\color{#009600}{k}}, where h{\color{#0000FF}{h}} represents a horizontal translation and k{\color{#009600}{k}} represents a vertical translation. y=(x+1)21y=(x(-1))2+(-1)\begin{gathered} y=(x+1)^2-1 \\ \Updownarrow \\ y=(x-({\color{#0000FF}{\text{-}1}}))^2+({\color{#009600}{\text{-}1}}) \end{gathered} In our case, we have h=-1{\color{#0000FF}{h}}={\color{#0000FF}{\text{-}1}} and k=-1.{\color{#009600}{k}}={\color{#009600}{\text{-}1}}. This means that the graph of y=f(x+1)1y=f(x+1)-1 is obtained by translating the graph of y=f(x)y=f(x) to the left 1{\color{#0000FF}{1}} unit and down 1{\color{#009600}{1}} unit.
Parent Function\text{Parent Function}

Horizontal Translation\text{Horizontal Translation}

Vertical Translation\text{Vertical Translation}

Thus, we conclude that the correct answer is option A.