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.