Question

Compare the graphs of each group of functions and list them in order from widest to narrowest. See pic attached

Answer 1

In general, for a parabola

`\begin{gathered} y=ax^2 \\ \end{gathered}`

For |a|=>1, the larger the value of |a| is, the narrower the parabola is; in contrast, if 0<|a|<1, the smaller |a| is, the wider the graph of the function will be.

Therefore, since |-5|=5, |-3|=3, and |-1|=1, we have that

`|-5|>|-3|>|-1|\ge1`

Thus, -5x^2 is the narrowest function of the three, followed by -3x^2 and -1x^2, as shown in the image below

From widest to narrowest, the order is -1x^2, -3x^2, and -5x^2