Function Transformations / Translations: Basic Rules .
We know right off the bat that we have a vertical reflection across the x-axis. What does this do to our y-values? It reverses them! Anything that once was positive is now negative, and vice versa. So let's
Next, we have a vertical stretch. Look at the blue vertex; . Look at the Red one, (-2,0.5). Our vertex had its y-value halved! (Keep in mind, we know it is a stretch, and not a translation because the roots [invariant points on the x-axis] have not changed.) So lets
Lastly, what else has this graph done? It moved left 3 units from to ! Let's factor that in;
Replace with .
Do your replacements and simplify it all back down to the form , and plug it into your graphing calculator to make sure!