6.7 other methods for solving

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6.7 other methods for solving

  1. 1. 6.7 Other Methods for Solving Quadratic Equations
  2. 2. 2 More Methods So far we can solve by: ◦ Factoring ◦ Taking square roots But, these only work for some equations! Two more ways are: ◦ The Quadratic Formula ◦ Graphing
  3. 3. The Quadratic Formula Works to solve ANY quadratic equation! Remember, standard form is: ax2 + bx + c = 0 Quadratic Formula: https://www.youtube.com/watch?v=YCuXiujC3KE
  4. 4. Example: Solve for x:
  5. 5. Example: Solve for x:
  6. 6. Example: Solve for x:
  7. 7. You Try! Solve for x:
  8. 8. Solving by Graphing Remember: a function’s zeros are its x-intercepts. Zeros happen where y = 0.
  9. 9. Solving To solve a quadratic equation in standard form, we can: 1. Change from “= 0” to “y = ” 2. Graph function on calculator. 3. Find x-intercepts.  Menu  Trace  Graph Trace
  10. 10. Example 1: Solve by graphing. Round to the nearest tenth.
  11. 11. Example 2: Solve by graphing:
  12. 12. Example 3: Solve by graphing:
  13. 13. How Many Solutions? Two Imaginary Solutions One Real Solution Two Real Solutions
  14. 14. You Try! Solve by graphing:

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