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April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
April 23, 2014
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April 23, 2014

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  • 1. Today:  Welcome Back  Notebook, pencil, calculator ready  Review for final exam and test
  • 2. Reminders:  All Khan Academy Due by 3:00 & 9:00  There will be a test on Friday. We will review today and tomorrow.  The unit on Quadratics is almost finished; we begin our unit on radicals tomorrow.  Next Khan will be given Monday.  Classwork: Show all work, and most importantly, complete & turn in.  We are reviewing for the final exam first, then our test Friday, including new material. Get your pencil, calculator, and WORK THE PROBLEMS!!
  • 3. Warm-Up/Final Exam Review:
  • 4. Warm-Up/Final Exam Review:
  • 5. Warm-Up/Final Exam Review:? Simplify:
  • 6. Warm-Up/Final Exam Review: Drawing a number line helps, especially with the negative numbers Which relation below is not a function? A. B.
  • 7. Quadratic Review/Test Prep:
  • 8. no 1. Without graphing, tell whether (3, 12) is on the graph of y = 2x2 – 5. Quadratic Review/Test Prep: 2. What is the vertex of the equation: 3. What method are you using to solve?
  • 9. Write a Quadratic Equation Given Roots
  • 10. Write a Quadratic Equation Given Roots If all you had were the roots of a quadratic equation. Could you write the equation that produced the roots? The roots of a quadratic equation are -2 and 6. Write a quadratic model with leading coefficient of 1. Work backwards: start with your answer x = -2 or x = 6 solutions/roots x + 2 = 0 or x – 6 = 0 equation for roots (x + 2)(x - 6) = 0 quadratic equation x² - 6x + 2x – 12 = 0 distribute using FOIL x² - 4x – 12 = 0 combine like terms This is the quadratic equation with roots {-2, 6}
  • 11. The roots of a quadratic equation are 7 and - 1. Write a quadratic equation with leading coefficient of 1. x - 7 = 0 or x + 1 = 0 equation for roots x = 7 or x = - 1 solutions/roots x² - 6x – 7 = 0 combine like terms Write a Quadratic Equation Given Roots
  • 12. A parabola crosses the y axis at -3 and 1. a. Write a quadratic function where x is a function of y: f(y) =b. find the AOS, vertex, then graph Write a Quadratic Equation Given Roots y2 + 2y - 3 Vertex is: -4,-1 Axis of Symmetry is: -4,-1 • • • • • Plot for y = 2, then graph
  • 13. Completing the Square 6x2 + 24x – 84 = 0
  • 14. Take the square root of both sides 2. When graphing, change the equation to: y = (x – 2)2 - 16 4x3 = 9x
  • 15. Rationalizing the Denominator
  • 16. We will start with a simple case of a radical in the denominator. This must be removed. Why? Rationalizing the Denominator By "rationalizing the denominator." (Changing the denominator from a radical number to a rational one.) This is done by removing the square root from the denominator. How can we make the denominator 2? It’s just a generally agreed upon thing in math, that’s all. How is it done? Simplify: Finally:
  • 17. Always factor out perfect squares Rationalizing the Denominator
  • 18. The Quadratic Formula Solve using the Quadratic Formula 3x2 = 5x - 2 x = 5 + 1 6 = 1, 2/3

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