Graphs of Functions `y=ax^2,y=ax^3`
Graph of the function `y=x^2` is parabola. To draw graph of the function `y=ax^2` we need to stretch (compress) parabola `y=ax^2` from x-axis with coeffcient `|a|`; if a<0, then we addtionally need to reflect graph of the function `y=|a|x^2` about x-axis.
On the figure to the left you can see graphs of the functions `y=ax^2` for `a=1;-1;3;-0.5`. All these graphs are called parabolas. When a>0 parabola is open upward, when a<0 parabola is open downward.
In a similar manner we can draw graph of the function `y=ax^3`, knowing graph of the function `y=x^3`. On the figure to the left you can see graphs of the function `y=ax^3` for `a=1;-1;3`.