Math Help Forum: Parabola questions

If an equation is y=0.5x^2 is it stretched or is it compressed?
Likewise y=5x^2 is it streched or compressed?
Thank you

Originally Posted by hannah_3

If an equation is y=0.5x^2 is it stretched or is it compressed?
Likewise y=5x^2 is it streched or compressed?
Thank you

A factor k in a function f(kx) is known as a "dilation." If [tex]k > 1[tex] then the x-axis is effectively "shrunk:" compared to the function f(x) the function f(kx) has a smaller horizontal "width." If then the x-axis is effectively "stretched:" compared to the function f(x) the function f(kx) has a larger horiztonal "width."

The best way to see this is with an example. I've attached your first problem below. Notice that the blue graph is wider than the red graph.

-Dan