Assignment Two

 

Horizontal Translation of a Parabola

 

Collaborative Effort by

 

Lucia Zapata and Claudette Tucker

Problem
Produce several ( 5 to 10) graphs of on the same axes using different values for d. Does varying d change the shape of the graph? the position?

Consider the following equation of the form, . Let's go to vary the constant d which yields the following graphs:

 

 

 

Note that varying d just translates each function along the x-axis. Varying d is a horizontal translation on the graph. Observe that there is not change in the shape, there only is a change in the position of the graphic.

Now again consider the equation . It follows that the derivative is

y' = 2(x-d).

There are some important details here.

First, for all values of d indicated in the graph above the zeros for the corresponding derivatives all pass through the line of symmetry.

Secondly, we can find an extreme value for . So, for y' = 2(x-d) , its zero is x = d. If we substitute in the original equation we would get y=-2. This means that an extreme value of the parabola is in y=-2.
We can see that the parabola moves through y=-2

 

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