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5.5 Completing the Square

5.5 Completing the Square. p. 282. 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 PTS!. So, it factors into this!.

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5.5 Completing the Square

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  1. 5.5 Completing the Square p. 282

  2. 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.

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

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

  5. Example: Solve by completing the square. x2+6x-8=0 • x2+6x-8=0 x2+6x=8 x2+6x+___=8+___ x2+6x+9=8+9 (x+3)2=17 Don’t forget: Whatever you add to one side of an equation, you MUST add to the other side!

  6. 5x2-10x+30=0 x2-2x+6=0 x2-2x=-6 x2-2x+__=-6+__ x2-2x+1=-6+1 (x-1)2=-5 3x2-12x+18=0 x2-4x+6=0 x2-4x=-6 x2-4x+__=-6+__ x2-4x+4=-6+4 (x-2)2=-2 More Examples!

  7. 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). Last Example! Write the quadratic function y=x2+6x+16 in vertex form. What is the vertex of the function’s graph?

  8. Assignment

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