1. Quadratics

2. y = x 2 Flips up because positive value Doesn’t move left or right on x axis. Stays at 0 Doesn’t move up or down y axis. Stays at 0 This is the “parent”.

3. y = 1/2 x 2 Flips up because negative value Doesn’t move left or right. Stays at 0 Doesn’t move up or down. Stays at 0 Makes parabola wider

4. y = -4x 2 + 2 Flips down because negative value Doesn’t move left or right. Stays at 0 Moves up 2 on y axis Makes parabola skinnier

5. y = 1/2 (x+3) 2 Flips up because negative value Moves left 3 on x axis Doesn’t move up or down. Stays at 0 Makes parabola wider

6. y = (x – 4) 2 + 5 Flips up because positive value Moves right 4 on x axis Moves up 5 on y axis

7. y = -(x + 2) 2 - 5 Flips down because negative value Moves left 2 on x axis Moves down 5 on y axis

8. y = - 3(x – 4) 2 + 9

9. y = x 2 – 7x + 12

10. y = (x – 3)(x + 6)

11. Quadratic Family Moves parent right 4 and up 5. This is the NEW vertex. x intercept: y intercept: vertex: D: R: none (0,21) (4,5) { y : y > 5}

12. y = x 2 – 7x + 12

13. HOW DO YOU FIND THE X INTERCEPTS? Set y = 0 0 = - 3(x – 4) 2 + 9 Minus 9 from both sides. -9 = - 3(x – 4) 2 Divide by -3 3 = (x – 4) 2 Square Root both sides 1.73 = x – 4 -1.73 = x - 4 Solve. (5.73, 0) and (2.27, 0)

14. HOW DO YOU FIND THE X INTERCEPTS? Set y = 0 Factor OR Quadratic Formula

15. HOW DO YOU FIND THE VERTEX? -b 2a This gives you the X COORDINATE of the vertex. To find the y, substitute this x into the original and evaluate. OR You Could Use the Midpoint of the x intercepts.

16. HOW DO YOU FIND THE VERTEX? Find the midpoint of the x intercepts. Then substitute that x into the original to find it’s y coordinate.

17. y = (x + 8)(x - 2)

18. HOW DO YOU FIND THE X INTERCEPTS? Set each factor equal to 0 and solve. (Take the opposite of them.) (-8,0) and (2,0) 6 th hour ends. They need rest of this and FF1

19. y = (3x + 2)(5x - 2)

20. Quadratic Family x intercept: y intercept: vertex: D: R: (-2/3, 0) (2/5, 0) (0,-4) (-2/15, -4.27) { y : y > -4.27}

21. y = x 2 – 7x + 12

22. Quadratic Family x intercept: y intercept: vertex: D: R: (4, 0) (3, 0) (0,12) (3.5, -.25 ) { y : y > -.25}

23. y = x 2 + 6x + 1

24. Quadratic Family x intercept: y intercept: vertex: D: R: NONE (0,1) { y : y > -8} Because there are NO x intercepts YOU MUST USE –b/2a to find the VERTEX!!! (-3, -8)

25. x 2 – 9

26. 4x 2 – 49

27. Factor (2x – 7)(2x + 7)

28. 16x 2 – 46x + 49

29. Factor (4x – 7)(4x - 7)

30. x 2 – 7x - 18

31. Factor (x + 9)(x - 2)

32. 12x 4 – 3x 3

33. Factor (3x 3 )(4x + 1)

34. (x + 10)(x - 2)

35. QUICK FOIL x 2 + 8x - 20

36. (x - 3)(x - 2)

37. QUICK FOIL x 2 - 5x + 6

38. (x – 5) 2

39. QUICK FOIL x 2 - 12x + 36

40. (3x + 2) 2

41. QUICK FOIL 9x 2 + 12x + 4