Solution Set for Basic Completion of the Square

Y=X²+12X-7

B=12
1/2B=6
(X+1/2B)²=(X+6)²

k=-7-6²=-43

Vertex form

Y=(X+6)²-43

Vertex is at: X=-6 and Y=-43

Y=X²-6X+6

B=-6
1/2B=-3
(X+1/2B)²=(X-3)²

k=6-(-3)²=-3

Vertex form

Y=(X-3)²-3

Vertex is at: X=3 and Y=-3

Y=X²+11X-1

B=11
1/2B=11.5
(X+1/2B)²=(X+11.5)²

k=-1-(11.5)²=-1-132.25=-133.25

Vertex form

Y=(X+11.5)²-133.25

Vertex is at: X=-11.5 and Y=-133.25

Y=X²-14X-31

B=-14
1/2B=-7
(X+1/2B)²=(X-7)²

k=-31-(-7)²=-31-49=-80

Vertex form

Y=(X-7)²-80

Vertex is at: X=7 and Y=-80

Y=X²-9x+4

B=-9
1/2B=-4.5
(X+1/2B)²=(X-4.5)²

k=4-(-4.5)²=4-20.25=-16.25

Vertex form

Y=(X-4.5)²-16.25

Vertex is at: X=4.5 and Y=-16.25