GRAPHING VERTICAL TRANSLATIONS OF PARABOLAS

Recall: Vertical Translations  When you add a constant to the end of the equation for a parabola, you translate it vertically.  If the constant is positive, the parabola is translated up (positively). If the constant is negative, the parabola is translated down (negatively).

Graphing Vertical Translations  What if you have the graph of a parabola, and you want to translate that graph vertically? How do you graph the new parabola?  Just move every point on the parabola the same distance vertically.

Example Here’s an example of a parabola that has been vertically translated. Each point on the new parabola is 5 higher than its corresponding point on the old one.

The Process 1. Figure out how far the parabola is translated 2. Graph the original parabola 3. Graph the translated parabola by translating each point.

Example Part 1  Say we want to graph y = x 2 – 3.  The first step is to figure out how much it’s translated from the basic parabola y = x 2.  Since we subtract three, the parabola is translated 3 units down.

Example Part 2 First, we’re going to graph the original parabola.

Example Part 3 Now we’ll graph the new parabola by moving each point 3 units down. We have our new graph!