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Algebra 2B - Chapter 6

Algebra 2B - Chapter 6. Quadratic Functions. 6-1: Graphing Quadratic Functions Learning Targets:. I can graph quadratics using five points. I can find max. and min. values. Graph of a quadratic function:. Plug x into the function to find y. This is where the graph makes its turn.

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Algebra 2B - Chapter 6

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  1. Algebra 2B - Chapter 6 Quadratic Functions

  2. 6-1: Graphing Quadratic FunctionsLearning Targets: I can graph quadratics using five points. I can find max. and min. values.

  3. Graph of a quadratic function: Plug x into the function to find y. This is where the graph makes its turn.

  4. Using the TI to Graph Know these function keys on your calculator: y = set window table max and min

  5. Example 1:Graph f(x)= 3x2 - 6x+ 7 Axis of symmetry: Direction of opening: Up / down? “a” value? Maximum / Minimum? Value: _____________ 1 4 (1, 4)

  6. Example 2:Graph f(x)= - x 2 + 6x- 4 Axis of symmetry: Direction of opening: Up / down? Maximum / Minimum? Value: _____________

  7. Lesson 6.1: Closing Can you graph quadratics using five points and/or your calculator? H.W. Practice 6.1 Can you find max. and min. values?

  8. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  9. Transparency 2a

  10. Algebra 2B - Chapter 6Lesson 6.6 Analyzing graphs of Quadratic Functions

  11. Lesson 6.6Learning Targets: I can graph quadratic functions in vertex form. I can write quadratic functions in standard and/or vertex form.

  12. Vertex Form Standard Form

  13. Exploration Activity

  14. Transparency 7 Click the mouse button or press the Space Bar to display the answers.

  15. Transparency 7a

  16. Algebra 2B - Chapter 6Lesson 6.3 Solving Quadratic Equations by factoring

  17. Lesson 6.3Objectives: • Solve quadratic equations by factoring • Write a quadratic equation with given its roots

  18. Review: Factoring Trinomials Any trinomial: Example: Perfect square trinomial: Example: Difference of two squares: Example: Hint: always check for GCF first! X – Box Method 5x2 -13x + 6 x2 + 12x + 36 y4 – z2

  19. Vocabulary Zero Product Property: For any real numbers a and b, if ab = 0, then either a = 0 or b = 0, or both a and b equal zero. To write a quadratic equation with roots p and q: Write the pattern: (x – p)(x – q) = 0

  20. Example 1: Solve by factoring • Set the equation equal to zero. • Factor out the GCF if possible. • Use another factoring method if possible. • Set the factor/s equal to zero. • Solve. 3x2 = 15x

  21. Example 2: Solve by factoring • Set the equation equal to zero. • Factor out the GCF if possible. • Use another factoring method if possible. • Set the factor/s equal to zero. • Solve. 4x2 - 5x = 21

  22. Write the quadratic equation given its roots Example 3: Write a quadratic equation with roots 3 and -5. Remember…(x – r)(x – p) = 0

  23. Write the quadratic equation given its roots Example 4: Write a quadratic equation with roots -7/8 and 1/3.

  24. Your Turn 1: Solve by factoring • Set the equation equal to zero. • Factor out the GCF if possible. • Use another factoring method if possible. • Set the factor/s equal to zero. • Solve. 5x2 + 28x – 12 = 0

  25. Your Turn 2: Solve by factoring • Set the equation equal to zero. • Factor out the GCF if possible. • Use another factoring method if possible. • Set the factor/s equal to zero. • Solve. 12x2 - 8x + 1 = 0

  26. Your Turn 3: Write a quadratic equation with roots -5.

  27. Your Turn 4: Write a quadratic equation with roots -4/9 and -1

  28. Lesson 6.3: Assessment • Check for Understanding: Closure 6.3 • Homework: Practice 6.3

  29. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  30. Transparency 4a

  31. Algebra 2B - Chapter 6Lesson 6.5 Solving Quadratic Equations by using the QuadraticFormula

  32. Lesson 6.5Learning Targets: I can: • Solve quadratic equations by using the Quadratic Formula • Use the discriminant to determine the number and types of roots

  33. Vocabulary Quadratic Equation: Quadratic Formula: Discriminant: Two rational roots: Two irrational roots: __________________ ____________________ __________________ ____________________ One rational root: Two complex roots _________________ __________________

  34. Example 1: 2x2 + 5x + 3 = 0 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  35. Example 2: 4x2 + 20x + 29 = 0 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  36. Example 3: 25 x2 - 40x = – 16 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  37. Example 4: x2 - 8x = -14 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  38. Your Turn 1: x2 + 2x - 35 = 0 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  39. Your Turn 2: x2 - 6x + 21 = 0 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  40. Your Turn 3: 3x2 +5x = 2 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  41. Your Turn 4: x2 - 11x + 24 = 0 a = ___ b = ___ c = ___ Discriminant: _________________________ Number & type of roots: ________________

  42. Lesson 6.5: Assessment • Check for Understanding: __________________________________ • Homework: ____6.5 Skills Practice________

  43. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

  44. Transparency 6a

  45. Algebra 2B - Chapter 6Lesson 6.2 Solving Quadratic Equations by graphing

  46. Lesson 6.2Learning Targets: • I can solve quadratic equations by graphing. (exact roots) • I can estimate solutions of quadratic equations by graphing. (approximate roots)

  47. Vocabulary x- intercepts of the graph solutions of the quadratic equation Cases: two real roots one real root no real roots , Ø

  48. Example: Not a point but the 2 places where the graph crosses the x-axis. This is called a double root. -3 is the answer twice.

  49. Old School or Vintage style: Part 1 : Exact rootsExample 1: Solve x2 + x – 6 = 0 by graphing. 2 -1 0 -2 -3 1 0 0 -6 -4 -4 -6 Exact Roots of the equation (or zeros of the function):________ & _______ -3 2

  50. Part 1 : Exact rootsYour Turn 1: Solve x2 - 4x– 5 = 0 by graphing. Exact Roots of the equation (or zeros of the function):________ & _______

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