### Horizontal Translations of Parabolas

We will examine what happens to the quadratic equation

as the variable d varies.

1) First off we'll start with d = 0. We will call this our base graph.

Where does the vertex seem to be on this graph? Make sure to verify your estimate. Where are the x-intercepts? Make sure to verify your answers.

2) Now we'll change d to 2 and observe what happens.

Careful, the positon of the origin has changed. Where is the vertex now? Estimate the x-intercepts. Make sure to verify all guesses either graphically or algebraically.

Describe the difference in the grpahs of the two parabolas.

3) Next, we'll set d = 4. Before we do that though, answer the following questions:

a) Where do you think the vertex will be?

b) Where do you think the x-intercepts will be?

All three graphs

4) Now, you've seen three graphs already. What about negative numbers? Make a conjecture of where the base graph will be when d = -3.

the d = -3 graph

5) Describe what will happen to

as d varies. In other words, where will the parabola be as d changes.

6) To check your answer to question 5, here's a video of the parabola as d varies from -5 to 5. Here's the Graphing Calculator file. As always, Graphing Calculator can be purchased from www.nucalc.com.

For those who absolutely haved to have the answers, they are here.

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