f(x)=1/4(x+2)^2-4.

i) explain how the parabola that is the graph of f can be obtained from the graph of y=x^2 by using appropriate translations and scalings.

ii) find the x-intercepts and y-intercept of the parabola.

$f(x)\:=\:\tfrac{1}{4}(x+2)^2-4$

i) Explain how the graph of $f(x)$ can be obtained from the graph of $y\,=\,x^2$
by using appropriate translations and scalings.
We know the graph of $y \:=\:x^2$
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The curve: $y \:=\:(x+2)^2$ is the previous graph moved 2 units to the left.
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The curve: $y \:=\:(x+2)^2-4$ is the previous graph moved 4 units down.
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The curve $y \;=\;\tfrac{1}{4}(x+2)^2-4$ "rises more slowly" . . . Hence, it is "wider".
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