How are the graphs $f(x)=x^2$ and $g(x)=1/2x^2-5$ related?

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Answer 1 · 2017-11-14T23:28:43

$f(x)$ is the parent graph of $g(x)$ . See below.

Basically, $f(x)$ is the original graph , while $g(x)$ is the result of $f(x)$ after it went through transformations .

Notice how in $g(x)$ , $x^2$ (which is the same as $f(x)$ ) is stretched by a factor of $1/2$ and moved downwards 5 units.

If we take away these two transformations on $g(x)$ , it'll look like $f(x)$ .

How are the graphs f(x)=x^2f(x)=x^2 and g(x)=1/2x^2-5g(x)=1/2x^2-5 related?