How do you sketch the graph of #y=-x^2+2# and describe the transformation?

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Answer 1 · 2018-02-21T03:59:24

See Explanation

Start by sketching its parent function. That is #y=x^2#

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

Next sketch #y=-x^2#. The #-# sign implies that the function #y=x^2# is flipped vertically over the #x-#axis.

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

Lastly, sketch #y=-x^2+2#. This means that we take all the points of the graph #y=-x^2# and translate them up #2# units.

The final graph will look like this:

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