"c" = ?
"a"=1 ; b is even
"a"is=1. : b is odd
"a"is not=1. : b is odd
"a"is not=1. : b is even
100

Given:  x2 + 12x +c

Find the value of "c" that creates a perfect square

trinomial

"c" = (1/2)x 12= 6     ;       6^2 =36

(x+6)^2

100

Convert y= x2 - 8x +5  to vertex form by

completing the square

y = (x-4)^2 - 11

100

Convert y= x2 - 7x +5  to vertex form by

completing the square

Y-5 = x2 - 7x

y-5 + 49/4 = x2- 7x + 49/4

y+ 29/4 = (x-7/2)2

y = (x-7/2)2 - 29/4

100

Convert y = -2x2+3x- 7 to vertex form by completing the square

y + 7 = -2x2+3x

y+ 7 = -2(x2 - 3x/2 )

y+7-(18/16) = -2( x2-3x/2 +9/16)

y+112/16 -18/16 = -2(x-3x/4)2

y +47/8 = -2(x-3x/4)

y = -2(x-3x/4)- 47/8

100

Convert y = 3x2 - 6x -8 to vertex form by completing the square

y+8 = 3x2-6x

y + 8 = 3(x2-2x)

y+8+3 = 3(x2-2x+1)

y+11 = 3(x-1)2

y = 3(x-1)2- 11

200

Given:  x2 - 20x +c

Find the value of "c" that creates a perfect square

trinomial

(1/2) x (-20) = -10. ;  (-10)^2 = 100

(x-10)^2

200

Convert y= x2 + 12x + 0  to vertex form by

completing the square

y = ( x+6)^2 - 36

200

Convert   y = x2 +13x +1  to vertex form by completing the square

Y-1 = x2 +13x

y-1 + 169/4 = x+13x +169/4

y+165/4 = (x+13/2)2

y = (x+13/2)2 - 165/4

200

Convert y = 3x2+3x- 11 to vertex form by completing the square

y+11 = 3x2+3x

y+11 = 3(x2+x )

y+11+3/4 = 3(x2+x +1/4)

y+ 47/4 = 3(x+1/2)2

y = 3(x+1/2)2 - 47/4

200

Convert y = x2/3 + 4x to vertex form by completing the square

y+0 = x2/3 +4x

y =0 = 1/3( x2+12x)

y +0+12 = 1/3( x2+12x+36)

y+12 = 1/3(x+6)2

y = 1/3(x+6)2-12

300

Given:  x2 + 11x +c

Find the value of "c" that creates a perfect square

trinomial

(1/2) x (11) = 11/2     ;    (11/2)^2 = 121/4

(x+11/2)^2

300

Convert y= x2 - 16x - 20  to vertex form by

completing the square

y = (x-8)^2 -84

300

Convert y = x2 + x - 3. to vertex by completing the square

Y+3 = x2 +x

y+3+1/4 = x2+x + 1/4

y+ 13/4 = (x+1/2)2

y = (x+1/2)2 - 13/4

300

Convert y = -x2 -5x. to vertex form by completing the square

y+0 = -x2-5x

y+0 = -(x2+5x)

y-25/4 = -(x+5x +25/4)

y -25/4 = -(x+5x/2)2

y = -(x+5x/2)2 + 25/4

300

Convert y = -2x2 -12x+9 to vertex form by completing the square

y -9 = -2x2-12x

y-9= -2(x2+6x)

y-9-18 = -2(x2+6x+9)

y-27 = -2(x+3)2

y = -2(x+3)2+27

400

Given:  x2 + (1/2)x +c

Find the value of "c" that creates a perfect square

trinomial

(1/2) x (1/2) = 1/4. ;  (1/16)^2 = 1/16

(x+1/4)^2

400

Convert y= x2 +2x -19  to vertex form by

completing the square

y = (x+1)^2 - 20

400

Convert y = x2+5x - 9 to vertex by completing the square

Y+9 = x2 +5x

y+9 + 25/4 = x2 +5x +25/4

y+ 61/4 = (x+5/2)2

y = (x+5/2)2 - 61/4

400

Convert y = x/2 - 9x +4. to vertex form by completing the square

y - 4 = x2/2 - 9x

y - 4 = 1/2( x2 - 18x)

y - 4+81/2 = 1/2 (x2 - 18x + 81)

y +73/2 = 1/2(x-9)2

y = 1/2(x-9)2 - 73/2

400

Convert y = 10x2+20x -17 to vertex form by completing the square

y =17 = 10x2+20x

y+17 = 10(x2+2x)

y+17+10 = 10(x2+2x+1)

y+27 = 10(x+1)2

y= 10(x+1)2-27

500

Given:  x2 -(2/5)x +c

Find the value of "c" that creates a perfect square

trinomial

(1/2) x (-2/5) = -1/5.   ;    (-1/5) ^2 = 1/25

(x-1/5)^2

500

Convert y= x2 +200x + 2500 to vertex form by

completing the square

(x+100)^2 - 7500

500

Convert. y = x2 - 15x -6. to vertex form by completing the square

Y+6 = x2 -15x

y+6 + 225/4 = x2- 15x + 225/4

y+ 249/4 = (x-15/2)2

y = (x-15/2)2 - 249/4

500

Convert y = -x2/2. + 7x -10 to vertex form by completing the square

y + 10 = -x2/2 +7x

y+10 = -1/2(x2 -14x)

y+10 - 49/2 = -1/2( x2-14x +49)

y - 29/2 = -1/2(x-7)2

y = -1/2(x-7)2 + 29/2

500

Convert y = -x2 - 8x +9 to vertex form by completing the square

y - 9 = -x2 - 8x

y-9 = -(x2+8x)

y-9 -16= -(x2+8x+16)

y-25 = -(x+4)2

y = -(x+4)2+25

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