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Quadratics

Quadratics. This is the “parent”. 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. Makes parabola wider. y = 1/2 x 2. Flips up because negative value. Doesn’t move left or right. Stays at 0.

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Quadratics

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  1. Quadratics

  2. This is the “parent”. 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

  3. Makes parabola wider y = 1/2 x2 Flips up because negative value Doesn’t move left or right. Stays at 0 Doesn’t move up or down. Stays at 0

  4. Makes parabola skinnier y = -4x2 + 2 Flips down because negative value Doesn’t move left or right. Stays at 0 Moves up 2 on y axis

  5. Makes parabola wider 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

  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 = x2 – 7x + 12

  10. y = (x – 3)(x + 6)

  11. 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} Quadratic Family

  12. y = x2 – 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 1.73 = x – 4 -1.73 = x - 4 Square Root both sides Solve. (5.73, 0) and (2.27, 0)

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

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

  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.) 6th hour ends. They need rest of this and FF1 (-8,0) and (2,0)

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

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

  21. y = x2 – 7x + 12

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

  23. y = x2 + 6x + 1

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

  25. x2 – 9

  26. 4x2 – 49

  27. Factor(2x – 7)(2x + 7)

  28. 16x2 – 46x + 49

  29. Factor(4x – 7)(4x - 7)

  30. x2 – 7x - 18

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

  32. 12x4 – 3x3

  33. Factor(3x3)(4x + 1)

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

  35. QUICK FOILx2 + 8x - 20

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

  37. QUICK FOILx2 - 5x + 6

  38. (x – 5)2

  39. QUICK FOILx2 - 12x + 36

  40. (3x + 2)2

  41. QUICK FOIL9x2 + 12x + 4

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