2.4 Solving Quadratic Equations using the Quadratic Formula

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2.4 Solving Quadratic Equations using the Quadratic Formula

  1. 1. 2.4 The Quadratic Formula February 26, 2013 2.4 The Quadratic Formula There are many ways to solve quadratic equations. All of them have their uses... Graphing Solutions - understanding what the graphical solutions look like and what properties to look for allows for easy and quick analysis. Factoring - will become more and more useful as you continue with pre-calculus for graphing functions to different degrees (x4, x8, etc); also very fast if you can easily and quickly factor a trinomial. Completing the Square - Very useful if given the equation in vertex form! The quadratic formula is a general solution to a quadratic equation. It works for ANY quadratic function in the form ax2 + bx + c = 0, a ≠ 0
  2. 2. 2.4 The Quadratic Formula February 26, 2013 E.g. Solve 3x2 + 5x - 2 = 0 The quadratic formula is also very useful when determining the nature (number) of roots (just like a graph!) We use a property called the discriminant
  3. 3. 2.4 The Quadratic Formula February 26, 2013 Discriminant # of Roots What it looks like b2  ­ 4ac b2  ­ 4ac b2  ­ 4ac E.G. How many roots does the following quadratic equation have?
  4. 4. 2.4 The Quadratic Formula February 26, 2013 E.g. Solve 9x2 + 12x = -4 Homework pg 254 #2ace, 3abde, 4ab, 8, 10

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