2.4 Solving Quadratic Equations using the Quadratic Formula
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2.4 Solving Quadratic Equations using the Quadratic Formula

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2.4 Solving Quadratic Equations using the Quadratic Formula Document Transcript

  • 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. 2.4 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. 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. 2.4 The Quadratic Formula February 26, 2013 E.g. Solve 9x2 + 12x = -4 Homework pg 254 #2ace, 3abde, 4ab, 8, 10