Solving the Quadratic Equation by Completing the Square

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features. - Factor using methods including common factors, grouping, difference of two squares, sum and difference of two cubes, and combination of methods. - Add, subtract, and multiply polynomials, - Explain how the multiplicity of the zeros provides clues as to how the graph will behave. - Sketch a rough graph using the zeros and other easily identifiable points. Students will factor polynomials using limited methods, perform operations (excluding division) on polynomials, and identify key features on a graph. - Add and subtract polynomials. - Multiply polynomials using an area model. - Factor polynomials using an area model. - Identify the zeros when suitable factorizations are available. - Identify key features of a graph. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 9 Learning Goal – ( HS.A-SSE.A.1, HS.A-SSE.A.2, HS.A-SEE.B., HS.A-APR.A.1, HS.A- APR.B.3, HS.A-REI.B.4) = Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features.

Complete the square when the leading coefficient is 1. How would you factor x 2 -6x+7=0?

Steps to “Completing the Square” 1.Subtract “c” from both sides of the equal sign. 2.Find ( 1 / 2 b) 2 3.Add that value to both sides of the equal sign. 4.Factor the perfect square trinomial. 5.Tip: Substitute the value of “ 1 / 2 b” into the parentheses to make a perfect square trinomial. (x + ___) 2 = {c + ( 1 / 2 b) 2 } 6.Take the square root of both sides. 7.Solve for x.

X 2 - 6x =-7 x 2 -6x+7=0 x 2 -6x+9=-7+9 Practice the steps to completing the square. Subtract 7 Make perfect square trinomial Add (½ b) 2 to each side.( 1 / 2 (-6)) 2 = 9

(x-3) 2 =2 Take sq. root Two Answers Add 3 to both sides Tip: Put ½ b into the ( ) with sign from original.

PRACTICE x 2 +5x-8=0 1. x 2 + 5x = 8 2.( 1 / 2 ∙5) 2 = 25 / 4 = 6¼ 3. x 2 + 5x + 25 / 4 = 8 + 6¼ 4.x 2 + 5x + 25 / 4 = 14¼ 5.(x + 5 / 2 ) 2 = 14¼ 6.x = ± √14 ¼ - 5 / 2

Practice: x 2 -4x+2=0 1. x 2 - 4x = ( 1 / 2 (-4)) 2 = 4 3. x 2 - 4x + 4 = x 2 - 4x + 4 = 2 5. (x - 2) 2 = 2 6. x = ± √2 + 2

Solve when the coefficient isn’t 1! 4x 2 -4x-15=0 Original: divide each term by 4 to get x 2 alone.

(x- ) 2 = 4 x =  2 + x = 2 ½ & -1 ½

What method is best?