GRAPHING REFLECTIONS OF PARABOLAS

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.

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.

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.

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.

Example: Step 1

Say we want to reflect the parabola defined by x2 + 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 x2 – 2x + 1.

Example: Step 2

Graph the original parabola if you don’t already have a graph of it.

Example: Step 3

Now, reflect the parabola over your chosen axis. Again, note corresponding points are equidistant from the y-axis.