Unit 3B part 1 Review

Complex Numbers

100

(9 + 5i) + (-4 +4i)

5 + 9i

200

(9 + 5i) - (8 - 10i)

1 + 15i

300

(4 - i)(2 - 3i)

5 - 14i

400

-7 -(6i)(12i) + (5 - 6i)

70 - 6i

500

(-6 - 4i) / (-2 - 4i)

(7 - 4i) / 5

Find "c"

100

Find the "c" that is needed to complete the square:

x^2 - 20x - 25 = 0

100

200

Find the "c"

x^2 - 5x - 18 = 0

6.25 or 25/4

300

Find the "c"

x^2 -19x + 35 = 0

90.25 or 361/4

400

Find "c"

2x^2 - 36x = -160

81

500

Find "c"

5x^2 - 80 = 10x

1

Solving by Completing the Square

100

Solve:

x^2 +8x +7 = 0

x = -7 and x = -1

200

Solve: 

x^2 + 6x = 16

x = -8 and x = 2

300

4x^2 +16x -84 = 0

x = -7 and x =3

400

Solve: 

3x^2 + 6x = 12

x = -1 +/- sqrt(5)

500

Solve:

5x^2 - 80 = 10x

x = 1 +/- sqrt(17)

Imaginary Solutions

100

x^2 - 4x + 5 = 0

x = 1 + 2i and x = 1- 2i

200

x^2 - 8x +185 = 0

x = 4 +13i  and x = 4 - 13i

500

2x^2 + 8x + 14 = 0

x = -2 + i(sqrt 3)  and x = -2 - i(sqrt 3)

Rewriting into vertex form

100

y = 3x^2 +12x +4

y = 3(x + 2)^2 - 8

200

y = 5x^2 - 20x - 2

y = 5(x - 2)^2 - 22

300

y = 2x^2 +8x + 6

y = 2(x + 2)^2 - 2

400

y = 3x^2 -3x -10

y = 3(x- 0.5)^2 - 10.75

500

y = 2x^2 +5x + 6

y = 2(x - 1.25)^2 + 2.875

or 

y = 2(x+ 5/4)^2 + 23/8