1. GRAPHING REFLECTIONS OF PARABOLAS

2. Review: Reflections  A reflection is the result of replacing x with –x or f(x) with –f(x).  The former causes a reflection over the y-axis, the latter causes a reflection over the x-axis.

3. Graphing a Reflection  What if you have the graph of a parabola, and you want to reflect that graph? How do you graph the new parabola?  Just flip the sign of all your x- or y-coordinates, depending on which axis you’re reflecting over.  If you reflect over the x-axis, flip the sign of y. If you reflect over the y-axis, flip the sign of x.

4. Example Here’s a parabola that’s been reflected over the x-axis. Note that corresponding points on the two parabolas are the same distance from the x-axis, but on different sides.

5. The Process 1. Determine which axis your parabola is flipped over. 2. Graph the original parabola. 3. Reflect the parabola to find the new one.

6. Example: Step 1  Say we want to reflect the parabola defined by x 2 + 2x + 1 over the y-axis.  To do this, we will have to replace x with –x in the equation and in the graph.  Although we won’t actually be using it, note that our new equation is x 2 – 2x + 1.

7. Example: Step 2 Graph the original parabola if you don’t already have a graph of it.

8. Example: Step 3 Now, reflect the parabola over your chosen axis. Again, note corresponding points are equidistant from the y-axis.