Completing the Square

1. Completing the Square To complete the square of a quadratic function use the following steps: 1.) Group the variable terms together. 2.) Look at the coefficient of the x-term, find half of that value and square it. The coefficient of the x-term is - 8; half of - 8 is - 4; - 4 squared is 16 3.) Add and subtract that squared amount inside the parentheses. 4.) Bring the “subtracted squared amount” out of the parentheses and add to the constant. The expression remaining inside the parentheses is a perfect square trinomial and can be factored into the product of a binomial times itself. 5.) The vertex is the point (4, -13); the axis of symmetry is the vertical line x = 4

2. Completing the Square Cont. If the leading coefficient is not 1 there is an additional step 1. a.) to be done 1.) Group the variable terms together. a) Factor the leading coefficient out of the variable terms 2.) Look at the coefficient of the x-term, find half of that value and square it. The coefficient of the x-term is 5/2; half of 5/2 is 5/4; 5/4 squared is 25/16 3.) Add and subtract that squared amount inside the parentheses. 4.) Bring the “subtracted squared amount” out of the parentheses and add to the constant; in this case remember to multiply it by the leading coefficient. The expression remaining inside the parentheses is a perfect square trinomial and can be factored into the product of a binomial times itself. 5.) The vertex is the point (-5/4, -73/8); the axis of symmetry is the line x = -5/4; narrow bowl.