1. Learning Goals & Scales

2. Identify the Quadratic Functions 1 2 3 4 5 6

3. I can identify quadratic functions from a graph. 1. I cannot correctly identify a quadratic function from a graph. 2. I can sometimes identify a quadratic function from a graph. 3. I can usually identify a quadratic function from a graph. 4. I can easily identify a quadratic function from a graph and explain how to distinguish it from other functions.

4. Identify the Quadratic Functions  y = 2x² + 3x – 7  f(x) = x²  y = 4x + 3  y =|x + 3|-4  f(x) = -x² - 9  y = (x – 5)² + 2  y = 12 X X X X

5. I can identify quadratic functions from an equation. 1. I cannot correctly identify a quadratic function from an equation. 2. I can sometimes identify a quadratic function from an equation. 3. I can usually identify a quadratic function from an equation. 4. I can easily identify a quadratic function from an equation and explain how to discern that.

6. Identify key features of a Parabola Identify:  The Vertex  The Minimum  The Y-Intercept  The Solution/s  The Axis of Symmetry  The Domain  The Range  Concavity (Open Up / Down)

7. I can identify key features of graphs. 1. I cannot identify any parts of a parabola. 2. I can sometimes identify some, but not all parts of a parabola. 3. I can identify most of the parts of a parabola. 4. I can easily identify all of the parts of a parabola, and can explain their interrelatedness.

8. Spot the Form y = (x – 3)² + 2 y = (x – 6)(x + 5) y = 4x² + 2x - 9 y = -2(x – 1)² + 2 f(x) = 3x² - 6 Vertex Form Vertex Form & Standard Form Standard Form Factored Form

9. I can identify whether a quadratic function is in standard, vertex, or factored form. 1. I cannot tell what form a quadratic equation is in. 2. I can identify some forms of quadratic equations. 3. I understand how to tell the difference and can usually identify each form. 4. I can easily identify which form an equation is in, and explain how I know.

10. Convert the quadratic from vertex to standard form. f(x) = 2(x-5)² -4 1. FOIL the argument 4. Combine Like Terms 3. Multiply by “a” 2. Combine Like Terms

11. I can convert a quadratic from vertex to standard form. 1. I cannot convert a quadratic from vertex to standard form. 2. I understand the procedure, but I cannot execute it. 3. I understand the procedure, and can execute it. 4. I understand the procedure, can execute it, and understand why I might want to do it.

12. Convert the quadratic from factored to standard form. f(x) = (x-5)(x + 6) 1. FOIL the argument 2. Combine Like Terms

13. I can convert a quadratic from factored to standard form. 1. I cannot convert a quadratic from factored to standard form. 2. I understand the procedure, but I cannot execute it. 3. I understand the procedure, and can execute it. 4. I understand the procedure, can execute it, and understand why I might want to do it.

14. Convert the quadratic from standard to vertex form. f(x) = x² - 4x - 5 1. A = a 2. h = -b/2a 3. k = f(-b/2a )

15. I can convert a quadratic from standard to vertex form. 1. I cannot convert a quadratic from standard to vertex form. 2. I understand the procedure, but I cannot execute it. 3. I understand the procedure, and can execute it. 4. I understand the procedure, can execute it, and understand why I might want to do it.

16. Convert the quadratic from standard to factored form. f(x) = x² - 4x - 5 1. (x – p)(x – q) 2. P and q are factors of AC that add up to B

17. I can convert a quadratic from standard to factored form. 1. I cannot convert a quadratic from standard to factored form. 2. I understand the procedure, but I cannot execute it. 3. I understand the procedure, and can execute it. 4. I understand the procedure, can execute it, and understand why I might want to do it.

18. Find key features from equations Find:Where Found:  The Vertex  The Minimum  The Y-Intercept  The Solution/s  The Axis of Symmetry  The Domain  The Range  Concavity (Open Up / Down) Vertex Form (h,k) (or Standard Form) Vertex Form @ k (or Standard Form) Standard Form @ (0, C) Factored Form @ p and q Vertex Form @ x = h (or Standard Form) Any Form @ (-∞, +∞) Vertex Form @ (-∞, k] or [k, +∞) Any Form up if a is positive, else down

19. Write a quadratic function given zeros. Given zeros of 4 and -5 Write a quadratic function in standard form with those zeros. 1. f(x) = a (x – p)(x – q) 2. FOIL together

20. I can write quadratic equations with given zeros. 1. I cannot write a quadratic from given zeros. 2. I understand the procedure, but I cannot execute it. 3. I understand the procedure, and can execute it. 4. I understand the procedure, can execute it, and understand why I might want to do it.

21. Solve By Factoring Factor the Binomial Factor the Trinomial y = 14x² - 7x y = x² + 5x - 6 0 = 14x² - 7x 0 = 7x(2x – 1) 7x = 0 or 2x - 1 = 0 77 +1 +1 x=0 or 2x = 1 2 2 x = ½ Solution: x = {0, ½ } 0 = (x + 6)(x – 1) (x + 6)= 0 or (x – 1) = 0 -6 -6 +1 +1 x = -6 x = 1 Solutions: x = {-6, 1}

22. H. Students will be able to solve quadratic equations by factoring using the Zero Product Property. 1. I cannot solve quadratic equations by factoring. 2. I can solve some quadratic equations by factoring with help. 3. I can solve any factorable quadratic equations by factoring with only minor errors. 4. I can easily solve factorable quadratic equations by factoring.

23. Solve by Completing the Square x² + 4x -7 = y x² + 4x -7 = 0 +7 x² + 4x = 7 x² + 4x + __= 7 + __ x² + 4x + 4 = 7 + 4 x² + 4x + 4 = 11 (x+2)² = 11 x+ 2 = ± √11 x = {-2+√11, -2-√11}

24. H. Students will be able to solve quadratic equations by completing the square. 1. I cannot solve quadratic equations by completing the square. 2. I can solve quadratic equations by completing the square with help. 3. I can solve quadratic equations by completing the square with only minor errors. 4. I can easily solve quadratic equations by completing the square.

25. I. Students will be able to use the discriminant to determine the nature of the roots of a quadratic equation. 1. I am not able to use the discriminant to determine the nature of the roots of a quadratic equation. 2. I can find the discriminant, but I cannot use it to find the nature of the roots of a quadratic equation. 3. I can find the discriminant, and I can use it to find the nature of the roots of a quadratic equation. 4. I can find the discriminant, and I can use it to find the nature of the roots of a quadratic equation, and I can explain why.

26. J. Students will be able to identify real and imaginary parts of complex numbers and perform basic operations. 1. I cannot identify real and imaginary parts of complex numbers and perform basic operations. 2. I can identify real and imaginary parts of complex numbers, but cannot perform basic operations. 3. I can identify real and imaginary parts of complex numbers and perform basic operations with only minor errors. 4. I can easily identify real and imaginary parts of complex numbers and perform basic operations.

27. K. Students will be able to solve quadratic equations over the complex number system. 1. I cannot solve quadratic equations over the complex number system. 2. I can solve quadratic equations over the complex number system with help. 3. I can solve quadratic equations over the complex number system with only minor errors. 4. I can easily solve quadratic equations over the complex number system.

28. L. Students will be able to solve a quadratic function with the quadratic formula. 1. I cannot solve a quadratic function with the quadratic formula. 2. I can solve a quadratic function with the quadratic formula with help. 3. I can solve a quadratic function with the quadratic formula with only minor errors. 4. I can easily solve a quadratic function with the quadratic formula.