1. Section 7.2 Solving Quadratic Equations by Completing the Square

2. 7.2 Lecture Guide: Solving Quadratic Equations by Completing the Square Objective 1: Determine the constant term in a perfect square trinomial.

3. A key to working the problems in this section is to recognize perfect square trinomials. Recall that: Square of a sum: Square of a difference:

4. Write each equation so the left side is expressed as the square of a binomial. 1.

5. Write each equation so the left side is expressed as the square of a binomial. 2.

6. Fill in the missing constant term that is needed to make each expression a perfect square trinomial. 3.

7. Fill in the missing constant term that is needed to make each expression a perfect square trinomial. 4.

8. Objective 2: Solve quadratic equations by completing the square. Rewrite the left side of each equation so that it is a perfect square, and then solve this equation by using extraction of roots. 5.

9. Objective 2: Solve quadratic equations by completing the square. Rewrite the left side of each equation so that it is a perfect square, and then solve this equation by using extraction of roots. 6.

10. Completing the Square Step 1. Write the equation with the _______________ term on the right side. Example: Step 2. Divide both sides of the equation by the coefficient of to obtain a coefficient of ______ for. Step 3. Take one-half of the coefficient of x, square this number, and add the result to _______________ sides of the equation.

11. Step 4. Write the left side of the equation as a perfect _______________. Example: Step 5. Solve this equation by extraction of _______________. Completing the Square

12. Solve the following equations using the method of completing the square. 7.

13. Solve the following equations using the method of completing the square. 8.

14. Solve the following equations using the method of completing the square. 9.

15. Solve the following equations using the method of completing the square. 10.

16. Solve the following equations using the method of completing the square. 11.

17. Solve the following equations using the method of completing the square. 12.

18. 13. Use the graph of to: (a) Solve (b) Solve (c) Solve

19. 14. Construct a quadratic equation in x that has the given solutions. (a) and

20. 14. Construct a quadratic equation in x that has the given solutions. (b) and

21. 15. A square picture is surrounded by a mat and then framed. The width of the square mat is 1.5 times the width of the picture. If the area covered by the mat is 145, determine the width of the picture. Round to the nearest tenth of an inch. (a) Identify the variable: Let w = the _______________ of the picture in inches. Let _________ = the ______________ of the mat in inches. (b) Write the word equation: Area covered by mat = Total area covered by mat and picture ­ ________________________

22. (c) Translate the word equation into an algebraic equation: ____________ = _______________ - ________________ (d) Solve this equation: 15. A square picture is surrounded by a mat and then framed. The width of the square mat is 1.5 times the width of the picture. If the area covered by the mat is 145, determine the width of the picture. Round to the nearest tenth of an inch.

23. (e) Write a sentence that answers the question: (f) Is this answer reasonable? 15. A square picture is surrounded by a mat and then framed. The width of the square mat is 1.5 times the width of the picture. If the area covered by the mat is 145, determine the width of the picture. Round to the nearest tenth of an inch.