The purpose of this lesson is for students to apply principles of transformations to their knowledge about circles in the coordinate plane. First, students recall the equation for a circle with a given center and radius. Next, students rewrite equations of a circle from the form to the form by completing the square. They then consider the structure of the equation in this form as they compare it to the transformations from an original circle . 

Finally, students directly compare the equation of a circle with the equation of a parabola to consider how changes to the equation affect the transformations on the function.

Note that a circle is not a function in one variable, and therefore cannot be written as . This course and previous courses have focused on functions in one variable, but a circle is a function in two variables written . Understanding the nuances of a function of 2 variables is beyond the scope of this course. It is sufficient for students to consider some of the similarities between the effects of transformations on the equation for a circle with the work they have done in earlier lessons concerning the effects of transformations on the equations for other functions.