Standard Form to Vertex Form
y = x2 + 6x + 5
y = (x2 + 6x) + 5 (Do Magic Formula (1/2 x B)2) (1/2 x 6)2 = 32 = 9
y=(x2 + 6x +9 −9)+5 (Multiply -9 to 1)
y=(x2 + 6x +9 −9)-9 + 5 (Square root +9)
y=(x+3)2−4
Vertex (-3, -4)
y=(x−2)2−9
y=(x−2)2−9 (Expand the vertex form)
y=(x2−4x+4)−9
y=x2−4x−5 (Two numbers that multiply -5, add to -4) (-5,1)
Final y=(x−5)(x+1)
y = (x-2)(x+3)
Use the foil method
y = x(x) + x(3) - 2(x) -2(3)
y = x2 + 3x − 2x − 6 (collect like term)
y = x2 + x − 6
y = x2 + 5x + 6
y = x2 + 5x + 6 ( find a number that multiply to 6 add 5) (2,3)
y=(x+2)(x+3)
Final y=(x+2)(x+3)
y = (x + 2)2 -3
y = (x + 2)2 -3 (expand)
y = x2 + 4x + 4 -3
y = x2 + 4x + 1
y = x2 - 2x + 3
y = x2 - 2x + 3
y = (x2 - 2x) + 3 next Do the magic formular (x\2)2
(-2\2)2 = 1
y = (x2 - 2x + 1 - 1) + 3 (times the -1 to 1)
y = (x2 - 2x + 1) -1 + 3
y = (x2 - 1)2 + 2
The vertex is (1, 2)
y=(x−4)2−1
y=(x−4)2−1 (expand it)
y=x2−8x+16−1 (collect like terms)
y=x2−8x+15 (two numbers multiply to 15 and add to -8) (it's -5 and -3)
y=(x−5)(x−3)
y=(x+2)2−9
y=(x+2)2−9
(x+2)2 = x2 + 4x +4
y = x2 + 4x + 4 − 9
= x2 + 4x − 5 (final answer)
y=3x2 +11x+6
y=3x2 +11x+6 (3×6=18)
Two numbers multiply to 18 and add to 11) (9,2)
y=3x2+9x+2x+6 (group them)
(3x2+9x)+(2x+6)
3x(x+3)+2(x+3)
Final answer; y=(3x+2)(x+3)
y=(x−4)2+7
y=(x−4)2+7 (expand)
y=x2−8x+16+7 (collect like terms)
Final y=x2−8x+23
y = 2x2 + 8x + 5
y = 2x2 + 8x + 5 (You have to factor it)
y = 2(x2 + 4x) + 5 (Do the Magic Number) (4\2)2=4
y = 2(x2 + 4x + 4 - 4) + 5 (you have to remove the -4) (times that by the 2 outside the bracket)
y = 2 (x2 + 2)2 - 8 + 5
y = 2 (x+2)2 −3
Vertex (-2, -3)
y=(x−3)2−4
y = (x−3)2−4 (expand the vertex form)
y = x2−6x+5 ( two numbers that multiply 5 and add to -6) (-5, -1)
y=(x−5)(x−1)
y=(x−1.5)(x+2)
y=(x−1.5)(x+2) do foil method
(x−1.5)(x+2) = x2+2x−1.5x−3 ( collect like terms)
Finals answer y=x2+0.5x−3
y=2x2 +6x+x+3
y=2x2 +6x+x+3 Group them
(2x2 + 6x) (x + 3) Factor each group
2x(x+3)+1(x+3)
= y=(2x+1)(x+3)
y=2(x+3)2 −5
y=2(x+3)2 −5
Y = 2 (x2+6x+9) - 5 (multiply all by 2)
y=2x2+12x+18−5 (collect like terms)
y=2x2+12x+13
y=1.5x2+3.6x+2.1
y=1.5x2 + 3.6x + 2.1 (factor it)
y=1.5(x2 + 2.4x) + 2.1 Do the magic formula (2.4\2)2 = 1.22 = 1.44
y=1.5(x2 + 2.4x + 1.44 − 1.44) +2.1
y=1.5 (x + 1.2)2 − 2.16 + 2.1
y=1.5(x + 1.2 )2 − 0.06
The Vertex is (-1.2, - 0,06)
y=−1.5(x+2)2+4
y=−1.5(x+2)2+4
y=−1.5(x2+4x+4) (multiply -1.5)
= y=−1.5x2−6x−6+4
Final: y=−1.5x2−6x−2
y = 2(x-4)(x+1\2)
(x-4)(x+1\2) = x2 + 1\2x - 4x - 2
= x2 - 7\2x - 2
y = 2(x2 - 7\2x - 2) multiply by 2
Final answer y=2x2−7x−4
y = − 3x2 + 12x −9
y = − 3x2 + 12x −9 ( factor them by-3)
y = −3 (x2−4x+3) (multiply by 3, add by -4) (-1, -3)
= x2−4x+3=(x−1)(x−3)
Final answer y=−3(x−1)(x−3)
y=1.5(x−2.2)2+3.6
y=1.5(x−2.2)2+3.6 (expand)
y = 1.5 (x2 − 4.4x + 4.84) + 3.6 (Multiply them by 1.5)
y = 1.5x2 −6.6x + 7.26 + 3.6 (collect like terms)
y=1.5x2−6.6x+10.86
y = 1\2x2 - x + 5\2
y = 1\2x2 - x + 5\2
y = 1\2 (x2 - 2x) + 5\2 (do the magic formula) (-2\2)2 = 1
y = 1\2 (x2 - 2x + 1 - 1) + 5\2 (times the -1 to 1\2)
y = 1\2 (x - 1)2 - 1\2 + 5\2
y = 1\2 (x - 1)2 + 2
The vertex (1, 2)
y = 1/2 (x - 3/4)2 + 5/2
y = 1/2 (x - 3/4)2 + 5/2 (expand the squared binomials)
y = 1/2 (x2 - 3/2x + 9/16) 5/2 (Multiply Everything with 1/2)
y = 1/2x2 - 3/4x - 9/32 + 5/2 (5/2 = x/32)(find the dinominator)(2x16=32, 5x16= 80)
5/2 = 80/32
Final answer: y = 1/2x2 - 3/4x + 89/32
y=1.5(x−2.2)(x+0.4)
y=1.5(x−2.2)(x+0.4)
First, expand (x−2.2)(x+0.4) Foil Method
(x−2.2) (x+0.4)
= x2 + 0.4x − 2.2x − 0.88
y=1.5 (x2 − 1.8x − 0.88)
Final answer y = 1.5x2 − 2.7x − 1.32
y=0.5x2+1.5x+1
y=0.5x2+1.5x+1 (multiply to 0.5, add to 1.0) (1.0 and 0.5)
y=0.5x2+x+0.5x+1 (group them)
(0.5x2+x)+(0.5x+1)
x(0.5x+1)+1(0.5x+1)
Final answer: y=(x+1)(0.5x+1)
y = 3/4 (x + 2/3)2
y = 3/4 (x + 2/3)2 (expand)
y =3/4 (x2 + 3/4x +4/9) - 7/5 (Multiply everything about 3/4)
= 4/3x2 + x + 3/1 - 7/5 Find the common dinominator its 15
5/15 - 21/15 = -16/15
FINAL form: y = 3/4x2 x + - 16/15