2. 5.5 Completing the Square p. 282

3. 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.

4. Rule for Completing the Square This is now a PTS! So, it factors into this!

5. Example: Find the value of c that makes this a PTS, then write the expression as the square of a binomial. x 2 -3x+c ► b=-3

6. Example: Solve by completing the square. x 2 +6x-8=0 ► x 2 +6x-8=0 x 2 +6x=8 x 2 +6x+___=8+___ x 2 +6x+9=8+9 (x+3) 2 =17 Don’t forget Don’t forget: Whatever you add to one side of an equation, you MUST add to the other side!

7. More Examples! ► 5x 2 -10x+30=0 x 2 -2x+6=0 x 2 -2x=-6 x 2 -2x+__=-6+__ x 2 -2x+1=-6+1 (x-1) 2 =-5 ► 3x 2 -12x+18=0 x 2 -4x+6=0 x 2 -4x=-6 x 2 -4x+__=-6+__ x 2 -4x+4=-6+4 (x-2) 2 =-2

8. 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).

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