Question

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

Answer 1

See Explanation

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]}