Hello, toplad!
$\displaystyle f(x)\:=\:\tfrac{1}{4}(x+2)^24$
i) Explain how the graph of $\displaystyle f(x)$ can be obtained from the graph of $\displaystyle y\,=\,x^2$
by using appropriate translations and scalings. We know the graph of $\displaystyle y \:=\:x^2$ Code:

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The curve: $\displaystyle y \:=\:(x+2)^2$ is the previous graph moved 2 units to the left. Code:

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The curve: $\displaystyle y \:=\:(x+2)^24$ is the previous graph moved 4 units down. Code:

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The curve $\displaystyle y \;=\;\tfrac{1}{4}(x+2)^24$ "rises more slowly" . . . Hence, it is "wider". Code:
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