4.12 Finding Standard Form by Completing the Square Circles and Parabolas Using Completing the Square to put equations into standard form Think Back to Geometry... The standard equation of a circle with center and radius is . ; Center ; The standard equation of a circle with center and radius is . ; Center ; Complete the Square to find the standard form of Circles and Quadratics CIRCLES Completing the Square will allow us to find the standard form for the equation of a circle. Suppose you are given an equation . If you have two variables then you will need to Complete the Square twice (once with each set of variables). First, group "like variables" on the left and the constants on the right Complete the square in each Parentheses Simplify This equation matches the standard form of a circle. Therefore, it is a circle with radius and center . QUADRATICS (PARABOLAS) The standard vertex form for a parabola is represents the vertex Notice the and are both squared in the circle equation above. If there is only 1 variable squared then there is a slightly different process for completing the square. You will also realize that it can't