How is the graph of $h (x) = 2 - x^{2}$ $h(x)=2-x^2$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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How is the graph of $h (x) = 2 - x^{2}$ $h(x)=2-x^2$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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Answer 1 · 2017-11-19T23:58:58

$h (x) = 2 - x^{2}$ $h(x)=2-x^2$ is the graph of $f (x) = x^{2}$ $f(x)=x^2$ reflected in the X-axis and then shifted up $2$ $2$ units.

Explanation:

If $f (x) = x^{2}$ $f(x)=x^2$
then $g (x) = - x^{2}$ $g(x)=-x^2$ is the reflection of $f (x)$ $f(x)$ in the X-axis
and
$h (x) = 2 - x^{2}$ $h(x)=2-x^2$ is (g(x) $shifted up$ 2# units

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How is the graph of $h (x) = 2 - x^{2}$ $h(x)=2-x^2$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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How is the graph of $h (x) = 2 - x^{2}$ $h(x)=2-x^2$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?