How is the graph of $h(x)=-x^2+8$ related to the graph of $f(x)=x^2$ ?

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Answer 1 · 2017-12-17T23:32:19

The graph has been reflected over the x-axis and translated 8 units up on the y-axis.

graph{x^2 [-10, 10, -5, 5]}
graph{-x^2 + 8 [-10, 10, -5, 5]}

This observation in the answer can be made based on the two graphs above.

How is the graph of h(x)=-x^2+8h(x)=-x^2+8 related to the graph of f(x)=x^2f(x)=x^2?