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

Feb 21, 2018

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]}