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Complete the Square
Solve for X
Translations
100

x2 + 4x + 9 = 0

(x + 2)2  + 5

100

(x - 1)2 = 6 

x = 1 +/- [sqrt6]

100

f(x) = x2 

move this formula up 3 

f(x) = x2 + 3

200

x2 - 10x + 13 = 0

(x - 5)2  - 12 = 0

200

(x + 5)2 = 12

x = -5 +/- 2[sqrt3]

200

f(x) = x2 + 4

move this equation 6 left

f(x) = (x + 6)2 + 4

300

x2 - 8x + 10 = 0

(x - 4)2 = 6

300

(x - 7)2 = 18

x = 7 +/- 3[sqrt2]

300

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

move this equation up 5 

f(x) = (x - 3)2 + 6

400

x2 - 7x + 15 = 0

( x - (7/2))2 = -15 + 49/4 

or 

( x - (7/2))2 = -11/4

400

2(x - 3)2 = 10 

x = 3 +/- [sqrt5]

400

f(x) = (x - 10)2

move this equation 4 down and 5 left

shrink by 

f(x) = (x - 5)2 - 4

500

2x2 + 8x - 8 = 0

(x + 2)2  = 8 

500

3(x - 10)2 = 21

x = 10 +/- [sqrt7]

500

f(x) = x2

move this equation down 6, right 5, and flip in the x-axis

f(x) = -(x - 5)2 - 6