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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
• 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