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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