1. 4.7: Completing the Square
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13.
15.
17.
19.
21.
23.
41.
2 Reals, Discriminant: 12
43.
2 Reals, Discriminant: 180
45.
1 Double Root, Discriminant: 0 A.
+16 B.
c < –100
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4.7: Completing the Square 1

2. Section 2.2 Revised ©2011, viet.dang@humble.k12.tx.us
Completing the Square
Section 2.2
Revised ©2011,
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4.7: Completing the Square

3. 4.7: Completing the Square
Steps
Put terms with variables on one side and CONSTANT to the other side
Make sure the side is in DESCENDING order
Standard Form, Ax2 + Bx + C = 0 where A = 1
Identify the coefficient which is raised to the first power, DIVIDE the term by 2, and SQUARE the number (it will always be positive)
ADD to both sides to the equation
Put the equation into FACTORED form (Vertex Form)
SQUARE ROOT both sides and cancel the binomial
Solve for x and check
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4.7: Completing the Square

4. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 1: Put terms with variables on one side and terms without variables onto other side
Make sure the side is in DESCENDING order
Standard Form, Ax2 + Bx + C = 0 where A = 1
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4.7: Completing the Square

5. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 2: Identify the coefficient which is raised to the first power and divide the term by 2
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4.7: Completing the Square

6. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 3: Take the second term, divide the term by 2, and square that number
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4.7: Completing the Square

7. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 4: Add to both sides to the equation
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4.7: Completing the Square

8. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 5: Put the equation into factored form (Vertex Form)
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4.7: Completing the Square

9. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 6: Square Root both sides and cancel the binomial
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4.7: Completing the Square

10. 4.7: Completing the Square
Example 1
Solve x2 – 4x + 3 = 0 using completing the square
Step 7: Solve and Check
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4.7: Completing the Square

11. 4.7: Completing the Square
Example 2
Solve x2 – 24x = 100 using completing the square
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4.7: Completing the Square

12. 4.7: Completing the Square
Your Turn
Solve x2 = 12x – 20 using completing the square
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4.7: Completing the Square

13. 4.7: Completing the Square
Example 3
Solve x2 – 4x = –2 using completing the square
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4.7: Completing the Square

14. 4.7: Completing the Square
Example 4
Solve 2x2 + 12x – 32 = 0 using completing the square
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4.7: Completing the Square

15. 4.7: Completing the Square
Example 5
Solve 2x2 – 6x = 5 using completing the square
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4.7: Completing the Square

16. 4.7: Completing the Square
Your Turn
Solve –6x + 2x2 = –1 using completing the square
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4.7: Completing the Square

17. 4.7: Completing the Square
Vertex Form
Equation: y = a(x – h)2 + k
The vertex is (h, k). Think of HONG KONG
a is the scalar.
FOIL the problem out. Don’t forget to multiply the scalar and factors.
REMINDER: To complete the square, the leading coefficient must be 1. Since the h and k are on the same side, you will take ½ of b, square it, add to the first part and SUBTRACT from the k.
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4.7: Completing the Square

18. 4.7: Completing the Square
Example 6
Given x2 + 4x = 5, convert to Vertex Form
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4.7: Completing the Square

19. 4.7: Completing the Square
Example 7
Given x2 – 4x = –13, convert to Vertex Form
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4.7: Completing the Square

20. 4.7: Completing the Square
Your Turn
Given x2 – 16x = –2, convert to Vertex Form
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4.7: Completing the Square

21. 4.7: Completing the Square
Example 8
Given y = 2x2 – 8x + 3, convert to Vertex Form
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4.7: Completing the Square

22. 4.7: Completing the Square
Example 9
Given 9x2 + 18x = –3, convert to Vertex Form
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4.7: Completing the Square

23. 4.7: Completing the Square
Your Turn
Given 2x = –6x, convert to Vertex Form
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4.7: Completing the Square

24. 4.7: Completing the Square
Example 10
Write a rule in transformation form for the quadratic function with the vertex is at the origin and passes through (2, 12).
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4.7: Completing the Square

25. 4.7: Completing the Square
Example 11
Write a rule in transformation form for the quadratic function with the vertex is at the (5, 2) and passes through (4, 5).
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4.7: Completing the Square

26. 4.7: Completing the Square
Your Turn
Write a rule in transformation form for the quadratic function with the vertex is at the (2, –5) and passes through (3, –11).
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4.7: Completing the Square

27. 4.7: Completing the Square
Assignment
Worksheet
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4.7: Completing the Square