Solving Quadratic Equations by Factoring. 43210 In addition to level 3, students make connections to other content areas and/or contextual situations.

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Solving Quadratic Equations by Factoring

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.

Zero-Product Property If ab=0, then either a=0, b=0 or both=0 States that if the product of two factors is zero then one (or both) of the factors must be zero.

x 2 -11x+24 (x - 8)(x – 3) Factor a trinomial

Factor Quadratic Equation x 2 -11x + 24 = 0 Then (x-8)(x-3)=0 Either x-8=0 or x-3=0 Solve x-8=0 x-3=0 x=3 x=8 Solution x = 3, 8

(2x+ )(x- )=0 (2x+5 )(x- 1 )=0 2x+5=0x-1=0 2x=-5x=1 2x 2 +3x-5=0

When you find the “x” values, you are finding out where the parabola crosses the x-axis when you graph the quadratic equation.

Make sure your quadratic is in standard form!!!!! 4x 2 =7x+2 4x 2 -7x-2=0 NOW FACTOR (4x+1)(x-2)=0 Keep x 2 positive

Solve for x 4x+1=0 4x=-1 x-2=0 x=2

Sometimes there is just one solution: x 2 -6x+11=2 -2 x 2 -6x+9 = 0 Perfect sq. tri. (x-3) 2 =0 x-3=0 x=3

Solve 4y 2 -18y=0 (2y)(2y-9)=0 2y=02y-9=0 Y=0 2y=9