Parabolic Function: Graph of y=ax^n

[batballbat]

how can the graph of the function y=ax^n be obtained from the graph of y=x^n if a is positive?negative

 

[mrmiller1]

If you graph two functions, y=x^2 and y=5x^2 you will notice the first graph appears "fatter" and the second graph is "skinnier".
As you increase the coefficient a the more narrow the graph becomes.
As you decrease the coefficient a the wider the graph becomes.
I would experiment with this concept until you notice a mathematical pattern by which you can predict the graph's appearance at any a.

 

[rckstr_scntst]

When a is negative, the graph is reflected about the x-axis. For example, the parabola y=-x^2 has the same shape as y=x^2, but is pointing down instead of up.