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Quiz 2 Feedback & Factoring Monday, September 16 Make sense of problems and persevere in solving them
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Quiz Review Work through any part of the quiz that you did not get completely correct to fix your errors. You may help each other with this.
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Factoring How many of you are familiar with factoring quadratics? How would you factor ax 2 + bx + c?
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Factoring f(x) = x 2 + 5x + 6 What is 1 x 6? What are factors of 6? Are there any that add up to 5? Check your work (hint: distribute!) 1 x 6 = 6 -1 x (-6) = 6 3 x 2 = 6 -3 x (-2) = 6 3 + 2 = 5 x2x2 3x 2x6 6 x +2 x +3 Answer: (x + 3) (x + 2)
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Factoring f(x) = x 2 – 5x + 6 What is 1 x 6? What are factors of 6? Are there any that add up to –5? Check your work (hint: distribute!) 1 x 6 = 6 -1 x (-6) = 6 3 x 2 = 6 -3 x (-2) = 6 -3 + (-2) = -5 x2x2 -3x -2x6 6 x -2 x -3 Answer: (x – 3) (x – 2)
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Factoring f(x) = x 2 + x – 6 What is 1 x -6? What are factors of 6? Are there any that add up to 1? Check your work (hint: distribute!) x2x2 +3x -2x-6 x -2 x +3 Answer: (x + 3) (x – 2) -1 x 6 = -6 1 x -6 = -6 -3 x 2 = -6 3 x -2 = -6 3 + (-2) = 1
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Factoring f(x) = 2x 2 + 2x – 12 What is 1 x -6? What are factors of 6? Are there any that add up to 1? Check your work (hint: distribute!) x2x2 +3x -2x-6 x -2 x +3 Answer: 2(x + 3) (x – 2) -1 x 6 = -6 1 x -6 = -6 -3 x 2 = -6 3 x -2 = -6 3 + (-2) = 1 = 2 (x 2 + x – 6)
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Factoring f(x) = 2x 2 + x – 6 What is 2 x -6? What are factors of -12? Are there any that add up to 1? Check your work (hint: distribute!) 2x 2 -3x +4x-6 -12 x +2 2x -3 Answer: (2x - 3) (x + 2) -3 + 4 = 1 -1 x 12 = -12 1 x -12 = -12 -2 x 6 = -12 2 x -6 = -12 -3 x 4 = -12 3 x -4 = -12
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Factoring Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2 Example: 4x 2 + 20x + 25 Is 4x 2 a perfect square? ▫What is “a”? Is 25 a perfect square? ▫What is “b”? Does 20x = 2ab? How would you use the general form to write the factored form?
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Practice You will be graded on the standard – Make sense of problems and persevere in solving them x 2 + 2x – 8 x 2 – 4x – 5 x 2 + 20x +100 2x 2 – 5x – 63 5x 2 – 55n + 50
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Converting Quadratics to Intercept Form Tuesday, September 17 Look for and express regularity in repeated reasoning
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Warm Up Factor: 5x 2 – 10x + 6 What are the zeros, vertex, and y-intercept of: f(x) = 5x 2 – 10x + 6
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Intercept Form The intercept form of a quadratic equation is the form of a quadratic equation by which you can easily tell the x intercepts of the quadratic equation: f(x)=a(x−p)(x−q) Axis of symmetry: x = p + q 2
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Converting to Intercept Form Standard Intercept f(x) = ax 2 + bx + c f(x) = a(x-p)(x-q) What differences do you notice about standard form and intercept form? If you had to guess, how do you think we could convert standard form into intercept form?
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Converting to Intercept Form Standard Intercept f(x) = ax 2 + bx + c f(x) = a(x-p)(x-q) f(x) = x 2 + 2x – 3 f(x) = 2x 2 + 2x – 6 f(x) = 4x 2 + 20x + 25
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Worksheet! Take out your worksheet and begin working on the problems You will be graded on the standard – Look for and express regularity in repeated reasoning
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Graphing Intercept Form Wednesday, September 18 Construct viable arguments and critique reasoning of others
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Warm Up Convert the following equation into intercept form: f(x) = 4x 2 + 16x – 48 What are the zeros and the axis of symmetry for the above equation?
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Graphing Intercept Form f(x) = 4(x + 6)(x – 2) What are the zeros? What is the axis of symmetry? What is the vertex? What is the y-intercept?
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Work with a partner! Convert the following equations in intercept form and graph them: f(x) = (x + 5) (x + 4) f(x) = -(x – 4) (x – 3) f(x) = 2(x – 3) (x + 5) f(x) = 2(2x + 3) (x – 2)
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Worksheet Take out today’s worksheet and begin working on the problems You will be graded on the standard – Construct viable arguments and critique reasoning of others
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Graphing Vertex Form Thursday, September 19 Construct viable arguments and critique reasoning of others
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Warm Up What are the zeros, vertex, and y-intercept of: f(x) = x 2 + 8x – 20
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Vertex Form The vertex form of a quadratic equation is written in terms of the vertex: f(x) = a(x – h) 2 + k Axis of symmetry: x = h
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Graphing Vertex Form f(x) = (x + 3) 2 + 4 What is the vertex? What is the axis of symmetry? What are the zeros?
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Work with a partner! Graph the following equations: f(x) = (x + 2) 2 – 3 f(x) = 2(x – 4) 2 – 1
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Worksheet Take out today’s worksheet and begin working on the problems You will be graded on the standard – Construct viable arguments and critique reasoning of others
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Practice for the Quiz Thursday, September 19
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Warm Up Convert the following equation into intercept form and graph the intercept form: f(x) = x 2 + 8x – 20 Graph the following equation in vertex form: f(x) = 4(x + 4) 2 + 4
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Take out your Worksheet! You will be graded on the standard – Makes sense of problems and perseveres in solving them
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Quiz Day Friday, September 20
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