Second Degree Equations

James Schaffer

 

Let’s graph functions of the form

on the same set of axes, where

.

 

 

At first observation, we can see that graphs whose coefficients are more positive experience a more drastic vertical stretch.¬† Since each graph experiences a y-intercept at exactly the same point, let’s explore the distinct x-values for which each graph yields a y-value of 1.

Let’s see if we can find a scaling of each a¬†that well help us achieve the desired corresponding x-value.

Now let’s put the coefficient of each entry in the third column in terms of its corresponding x-value in the second column.

 

 


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