College Algebra

Chapter 11.2

The Square Root Property and Completing the Square Day 2

Bell Ringer Solve the following quadratic equations 1. (x – 3)2 = -16

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2. (x + 2)2 = 12

Name______________________________________________________ Date________________________ Per._______ College Algebra Chapter 11.2 The Square Root Property and Completing the Square Day 2 Notes Today’s Objectives • I can complete the square for an expression of the form x2 + bx. (9-12.SSE.3(a), 9-12.IF.8) • I can solve a quadratic equation by completing the square. (9-12.SSE.3(a))

Completing the Square a)

c)

Complete the product sum box:

b)

Complete the product sum box:

-15

81

-3

18

Complete the product sum box:

5

d)

Complete the product sum box:

5

-3

10

e)

-6

Complete the product sum box:

Must be equal

g)

Must be equal

-16

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Complete the product sum box:

Must be equal

Must be equal

20

B. Fill in the Blanks a) 2

x + 6 x + 9 = ( ________ )

b) 2

x 2 − 12 x + 36 = ( ________ )

c)

2

d) 2

x + 22 x + _______ = ( x + 11)

2

x 2 − 30 x + _______ = ( x − 15)

e)

2

f) 2

x − 18 x + _______ = ( _________ )

2

x 2 + 4 x + _______ = ( __________ )

Solve a Quadratic Equation by Completing the Square Solve by USING THE SQUARE ROOT PROPERTY a) w2 + 2w = 0

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b)

z2 – 16z = 0

2

Name______________________________________________________ Date________________________ Per._______ College Algebra Chapter 11.2 The Square Root Property and Completing the Square Day 2 Assignment All radical answers must be in simplified radical form.

Fill in the blanks 1.

2.

3.

a2 + 12a + ______ = (_________)2

c2 – 18c + ______ = (_________)2

k2 – 16k + ______ = (_________)2

4.

5.

6.

j2 + 8j + ______ = (_________)2

n2 – 6n + ______ = (_________)2

r2 + 3r + ______ = (_________)2

Solve using the square root property. 7. a2 – 30 = 0 8.

10.

( c + 3)

2

− 4 = −29

11.

h2 + 14 = -23

( d + 2)

2

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− 7 = 13

2

9.

( q − 7)

12.

20 = ( 2 w + 1)

=1

2

Do NOT use a calculator for these problems.

Perform the indicated operation. 16.

( 4 + 2i ) + ( −7 + 8i )

17.

( 5 − 8i ) − ( 2 − 6i )

18.

6i ( 2 − 7i )

19.

( 5 − 4i )( 3 + 6i )

20.

( 2 − 3i )( 2 + 3i )

21.

4 + 3i 3−i

24.

i132

Simplify. 22.

i 38

23.

i 97

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25.

i 207