Quiz 2 Feedback & Factoring Monday, September 16 Make sense of problems and persevere in solving them

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.

Factoring How many of you are familiar with factoring quadratics? How would you factor ax 2 + bx + c?

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) = = 5 x2x2 3x 2x6 6 x +2 x +3 Answer: (x + 3) (x + 2)

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) = (-2) = -5 x2x2 -3x -2x6 6 x -2 x -3 Answer: (x – 3) (x – 2)

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 = x 2 = -6 3 x -2 = (-2) = 1

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 = x 2 = -6 3 x -2 = (-2) = 1 = 2 (x 2 + x – 6)

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 x +2 2x -3 Answer: (2x - 3) (x + 2) = 1 -1 x 12 = x -12 = x 6 = x -6 = x 4 = x -4 = -12

Factoring Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2 Example: 4x x + 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?

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 x x 2 – 5x – 63 5x 2 – 55n + 50

Converting Quadratics to Intercept Form Tuesday, September 17 Look for and express regularity in repeated reasoning

Warm Up Factor: 5x 2 – 10x + 6 What are the zeros, vertex, and y-intercept of: f(x) = 5x 2 – 10x + 6

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

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?

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 x + 25

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

Graphing Intercept Form Wednesday, September 18 Construct viable arguments and critique reasoning of others

Warm Up Convert the following equation into intercept form: f(x) = 4x x – 48 What are the zeros and the axis of symmetry for the above equation?

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?

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)

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

Graphing Vertex Form Thursday, September 19 Construct viable arguments and critique reasoning of others

Warm Up What are the zeros, vertex, and y-intercept of: f(x) = x 2 + 8x – 20

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

Graphing Vertex Form f(x) = (x + 3) What is the vertex? What is the axis of symmetry? What are the zeros?

Work with a partner! Graph the following equations: f(x) = (x + 2) 2 – 3 f(x) = 2(x – 4) 2 – 1

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

Practice for the Quiz Thursday, September 19

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

Take out your Worksheet! You will be graded on the standard – Makes sense of problems and perseveres in solving them

Quiz Day Friday, September 20