1. Chapter 6.4 Completing the Square Standard & Honors
Algebra II Mr. Gilbert
Chapter 6.4
Completing the Square
Standard & Honors
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2. Agenda
Warm up
Homework
Check your answers
Lesson
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3. Topic: Completing the Square
Example 1 Equation with Rational Roots (2)
Example 2 Equation with Irrational Roots (4)
Example 3 Complete the Square (3)
Example 4 Solve an Equation by Completing the Square (3)
Example 5 Equation with a  1 (3)
Example 6 Equation with Complex Solutions (4)
You will need a graphing calculator for this section.
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Lesson 4 Contents

4. Solve by using the Square Root Property.
Original equation
Factor the perfect square trinomial.
Square Root Property
Subtract 7 from each side.
Write as two equations. or
Solve each equation.
Answer: The solution set is {–15, 1}.
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Example 4-1a

5. Solve by using the Square Root Property.
Answer: {3, 13}
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Example 4-1b

6. Solve by using the Square Root Property.
Original equation
Factor the perfect square trinomial.
Square Root Property
Add 5 to each side.
Write as two equations. or
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Example 4-2a

7. Subtract 12 from each side.
Answer: The exact solutions of this equation are and The approximate solutions are 1.5 and Check these results by finding and graphing the related quadratic function.
Original equation
Subtract 12 from each side.
Related quadratic function
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Example 4-2a

8. Check Use the ZERO function of a graphing calculator
Check Use the ZERO function of a graphing calculator. The approximate zeros of the related function are 1.5 and 8.5.
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Example 4-2a

9. Solve by using the Square Root Property.
Answer:
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Example 4-2b

10. Step 2 Square the result of Step 1.
Find the value of c that makes a perfect square. Then write the trinomial as a perfect square.
Step 1 Find one half of 16.
Step 2 Square the result of Step 1.
Step 3 Add the result of Step 2 to
Answer: The trinomial can be written as
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Example 4-3a

11. Find the value of c that makes. a perfect square
Find the value of c that makes a perfect square. Then write the trinomial as a perfect square.
Answer: 9; (x + 3)2
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Example 4-3b

12. Solve by completing the square.
Notice that is not a perfect square.
Rewrite so the left side is of the form
Since
add 4 to each side.
Write the left side as a perfect square by factoring.
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Example 4-4a

13. Subtract 2 from each side.
Square Root Property
Subtract 2 from each side.
Write as two equations. or
Solve each equation.
Answer: The solution set is {–6, 2}.
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Example 4-4a

14. Solve by completing the square.
Answer: {–6, 1}
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Example 4-4b

15. Solve by completing the square.
Notice that is not a perfect square.
Divide by the coefficient of the quadratic term, 3.
Add to each side.
Since
add to each side.
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Example 4-5a

16. Write the left side as a perfect square by factoring
Write the left side as a perfect square by factoring. Simplify the right side.
Square Root Property
Add to each side.
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Example 4-5a

17. Answer: The solution set is
Write as two equations. or
Solve each equation.
Answer: The solution set is
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Example 4-5a

18. Solve by completing the square.
Answer:
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Example 4-5b

19. Solve by completing the square.
Notice that is not a perfect square.
Rewrite so the left side is of the form
Since
add 1 to each side.
Write the left side as a perfect square by factoring.
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Example 4-6a

20. Subtract 1 from each side.
Square Root Property
Subtract 1 from each side.
Answer: The solution set is Notice that these are imaginary solutions.
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Example 4-6a

21. Check. A graph of the related function shows that the
Check A graph of the related function shows that the equation has no real solutions since the graph has no x-intercepts. Imaginary solutions must be checked algebraically by substituting them in the original equation.
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Example 4-6a

22. Solve by completing the square.
Answer:
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Example 4-6b

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End of Lesson 4

24. Homework Review
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25. Homework - Honors See Syllabus 6.4
Pg multiples of 3, 49,50,52
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26. Homework
See Syllabus 6.4
Pg odd
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