Algebra II Honors PODHomework: p. 102 1-11 odds, 13-23 odds(you must use completing the square), and 77, 83

Find all real solutions for the following:

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a) x+ 3( ) x − 3( ) = 0

b) x2 +1 = 0

c) x − 5( ) x+ 2( ) = 0

d) x+ 4( )2 = 0

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a) x =3,− 3

b) noreal solution

c) x =5,− 2

d) x = −4

Zero-Product PropertyAB = 0 if and only if A = 0 or B = 0.

Quadratic equations have the form:

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y = ax2 +bx+ c

The roots of a quadratic equation are the x values that make the y value equal zero.

In the equation a, b and c are real and a ≠ 0.

Match each equation to its graph on the board.

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a) y = x2 +1

b) y = x2 − 3x −10

c) y = x2 − 9

d)y = x2 + 8x+16

Completing the Square

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x2 = 278

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x = ± 278

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x+ 3( )2 = 7

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x+ 3 = ± 7

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x = −3± 7

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x2 − 8x+ 7 = 0

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x − 7( ) x −1( ) = 0

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x = 7, 1

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x2 − 8x+ 7 = 0Let’s solve another way.

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x2 − 8x = − 7

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x2 − 8x+ 16 = − 7 +16

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x − 4( )2 = 9

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x − 4 = ± 9

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x = 4 ± 3

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x =7, 1

Completing the square for

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ax2 +bx+ c = 0

1) Subtract c.2) Divide by a.

3) Add to both sides of the equation.

4) Factor.5) Take the square root of both sides.6) Solve for x.€

12⋅ba

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Even answers from page 102.

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14) 2 ± 2 20) −1 or 19

16)12or −

72

22) 1±2 3

3

18)52

±212

24)12or

14

Algebra II H PODHomework: p. 102 25-59 odds, 69, 71, 82Solve the following by completing the square.

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ax2 +bx+ c = 0

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x =−b± b2 − 4ac

2a

This is called the Quadratic Formula.

Any quadratic equation can be solved using this formula.

Solve using the quadratic formula.

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5x2 +13x − 6 = 0

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a = 5, b =13, c =− 6

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x =−b± b2 − 4ac

2a

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x =−13± 132 −(4)(5)(−6)

2(5)

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x =−13± 169 +120

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x =−13± 289

10

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x =−13±17

10

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x =25

, − 3

Opposite of b, Opposite of b

Plus or minus square root, Plus or minus square root

b squared minus 4ac, b squared minus 4ac

Over 2a, Over 2a

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x =−b± b2 − 4ac

2a