Completing the Square.

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Solving Quadratic Equations by Completing the Square

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Presentation transcript:

Completing the Square

What is completing the square used for? Completing the square is used for all those not factorable problems!! It is used to solve these equations for the variable.

Rule for Completing the Square This is now a PERFECT SQUARE TRINOMIAL! So, it factors into this!

Example: Find the value of c that makes this a perfect square, then write the expression as the square of a binomial. x2-3x+c b=-3

Example: Solve by completing the square. x2+6x-8=0 Don’t forget: Whatever you add to one side of an equation, you MUST add to the other side!

Last Example. Write the quadratic function y=x2+6x+16 in vertex form Last Example! Write the quadratic function y=x2+6x+16 in vertex form. What is the vertex of the function’s graph? y=x2+6x+16 y-16=x2+6x y-16+__=x2+6x+__ y-16+9=x2+6x+9 y-7=(x+3)2 y=(x+3)2+7 If the equation, in vertex form, is y=(x+3)2+7, then the vertex must be (-3,7).