Kathye P. answered • 10/01/12

Math Geek, passionate about teaching

The "translation" refers to how the graph of the equation is changed from the graph of the basic equation, y=x^{2}.

The number added or subtracted inside the parentheses tells us that graph moves left or right. In this case the -4 tells us that it **shifts to the right 4 units**. (A number added or subtracted outside the parentheses indicates movement up or down; negative would be down.)

The number in front of the parentheses (which gets multiplied by x^{2}) tells us two things: the sign of the number tells us whether the parabola opens up or down, and the number tells us about the vertical stretch. In this case, the negative sign means **the parabola opens down, and it is stretched vertically by a factor of 2. **

The words in bold describe the translation. I like to graph the equation with my students so they can actually see these changes too.

Hope this helps!

Kathye