CPM Homework Help : INT3 Problem 10-195

Complete the square to write the equation $x^{2} + y^{2} - 4x - 16 = 0$ in graphing form and sketch a graph. What is the equation of the parent graph and how has it been transformed?

Step 1:

Gather the $x$ terms together and move the constants to the right side of the equation.

$\left(x^{2} − 4x + ?\right) + y^{2} = 16$

Step 2:

Determine what value will complete the square and add it to both sides of the equation.

$\left(x^{2} − 4x + 4\right) + y^{2} = 16 + 4$

Step 3:

Factor and identify the center of the circle and the radius.

$\left(x − 2\right)^{2} + y^{2} = 20$