4.6 Completing the Square

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  • 1. 4.6 COMPLETING THE SQUARE
  • 2. SOLVING BY FINDING SQUARE ROOTS
    • Solving equations of the form
      • Isolate the variable
      • “ Undo the Square” by taking the square root of both sides
      •  Don’t forget: when you take the square
      • root your solution is ±
  • 3. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
  • 4. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
  • 5. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS Note: No real number squared is equal to – 5, so the equation does not have a real number solution
  • 6. SOLVING A PERFECT SQUARE TRINOMIAL
    • Remember that a perfect square trinomials are of the form:
    • Sometimes they can be set equal to a constant
  • 7. SOLVING A PERFECT SQUARE TRINOMIAL
    • When a perfect square trinomial is set equal to a constant:
      • Factor the trinomial
      • Take the square root of both sides
      • Solve for the value of the variable
  • 8. EXAMPLE: SOLVE EACH EQUATION
  • 9. EXAMPLE: SOLVE EACH EQUATION
  • 10. COMPLETING THE SQUARE
    • If is part of a perfect square trinomial, we can find a constant c so that is a perfect square trinomial.
    • This is a process called completing the square
  • 11. COMPLETING THE SQUARE
    • We can form a perfect square trinomial
    • from by adding
  • 12. COMPLETE THE SQUARE
    • Find the value of
    • Add the value to the expression, this completes the square
  • 13. EXAMPLE: COMPLETE THE SQUARE
  • 14. EXAMPLE: COMPLETE THE SQUARE
  • 15. SOLVING AN EQUATION BY COMPLETING THE SQUARE
    • Rewrite the equation so it is of the form
    • Complete the Square: Add to both sides
    • Factor the prefect square trinomial
    • Take the square root of both sides
    • Solve for the variable
  • 16. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
  • 17. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
  • 18. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
  • 19. HOMEWORK
    • P 237 #1 – 8, 12 – 45 odd