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4.7A Complete the Square Algebra II
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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.
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Rule for Completing the Square
Please note: a=1 This is now a PST! So, it factors into this!
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Example 1: Find the value of c that makes this a PST, then write the expression as the square of a binomial. x2-3x+c b=-3
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Example 2: 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!
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Examples 3.) 5x2-10x+30=0 x2-2x+6=0 x2-2x=-6 x2-2x+__=-6+__
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4-7B Writing Quadratic Functions into Vertex form
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Example 1 Write the quadratic function y=x2+6x+16 in vertex form
Example 1 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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Example 2 Write the quadratic function y= 3x² - 6x -15 in vertex form. What is the vertex of the function’s graph?
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Assignment
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