Explain how the graph of each given function is a transformation of the graph of y=x^2. The transformation is y=-2x^2. I know it is reflected over the x-axis, but how much does it stretch or shrink?

Question

Explain how the graph of each given function is a transformation of the graph of  y=x^2. The transformation is y=-2x^2. I know it is reflected over the x-axis, but how much does it stretch or shrink?

anonymous · Answer

Well, think about  $ y = -2x^2 $  as the "reflection" of  $ y = 2x^2 $
Now. $y=2x^2$ is basically $ y= x^2 $ with all values doubled. This means, for every $x$ you plug into $x^2$ in $2x^2$ you'll get a double value.
This means $2x^2$ is vertically stretched, as all values are doubled.. and $ y = -2x^2 $ is both vertically stretched and "reflected".

anonymous · Answer

I know it is stretched, but by how much compared to y=x^2?

anonymous · Answer

doubled

anonymous · Answer

Oh, so the answer would just be that the function is reflected over the x-axis and is stretched by double? Thanks!

anonymous · Answer

or stretched by factor of 2... Maybe you could compare with an example exercise to see how they want the answer to be like.

anonymous · Answer

Alright I will, thanks again!

anonymous · Answer

Sure np