Solve by Square Roots
Solve by Completing the Square
Standard to Vertex Form
Solve by Quadratic Formula
Discriminants
100

5u2 + 20 = 110

+- 3 rt 2

100

x2 + 16x + 54 = 0

-8 +- rt 10

100

y = x2 + 6x + 11

y = (x+3)2 + 2

vertex: (-3, 2)

AoS: x = -3

100

3x2 + 4x - 3 = 0

-2 +- rt 13 / 3

100

4m2 - 2m = 0

D = 4, 2 solutions

200

0 = 3w2 - 84

+- 2 rt 7
200

n2 + 20n + 75 = -9

-10 +- rt 184

200

y = x2 + 4x + 5

y = (x+2)2 + 1

vertex: (-2, 1)

AoS: x = -2

200
7x2 + 6x + 1 = 0 

x = -3 +- rt 2 / 7

200

9n2 - 8n - 3 = 0

D = 172, 2 solutions

300

7w2 + 21 = 77

+- 2 rt 2

300

x2 + 18x - 23 = -4

-9 +- 3 rt 11

300

y = x2 + 8x + 14

y = (x+4)2 - 2

vertex: (-4, -2)

AoS: x = -4

300

3x2 - 5x = 3

x = 5 +- rt 61 / 6

300

5p2 - 7p + 11 = 2

D = -131, NRN

400

(y + 2)2 + 34 = 7

NRN

400

x2 - x - 30 = 0

x = 6, -5
400

y = -2x2 - 16x - 36

y = -2(x+4)2 - 4

vertex: (-4, -4)

AoS: x = -4

400
2x2 = -x + 9

x = -1 +- rt 73 / 4

400

3x2 - 2 = 7x + 6

D = 145, 2 solutions

500

(y - 3)2 + 6 = 24

3 +- 3 rt 2

500

m2 - 19m - 66 = 0

m = 22, -3

500

y = -3x2 - 6x - 2

y = -3(x+1)2 + 1

vertex: (-1, 1)

AoS: x = -1

500

5x2 - 9x = -2

x = 9 +- rt 41 / 10

500

-8b2 - 7 = -4b2

D= -112, NRN

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