body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Dashboard

Core Connections Algebra 2, 2013 View details

1. Section 7.1

Finish the assignment

Continue to next subchapter

Exercise 82 Page 336

Practice makes perfect

When we complete the square, the coefficient to x^2 has to be 1. Therefore, before we can complete the square, we must first divide both sides by 3.

y=3x^2-18x+26 ⇓ y/3=x^2-6x+26/3Now we can complete the square by adding the square of half the coefficient to x to both sides of the equation.

y/3=x^2-6x+26/3

AddEqn

LHS+(-6/2)^2=RHS+(-6/2)^2

y/3+(-6/2)^2=x^2-6x+26/3+(-6/2)^2

▼

Simplify

NegBaseToPosBase

(- a)^2=a^2

y/3+(6/2)^2=x^2-6x+26/3+(6/2)^2

CalcQuot

Calculate quotient

y/3+3^2=x^2-6x+26/3+3^2

CommutativePropAdd

Commutative Property of Addition

y/3+3^2=x^2-6x+3^2+26/3

SplitIntoFactors

Split into factors

y/3+3^2=x^2-2(x)(3)+3^2+26/3

FacNegPerfectSquare

a^2-2ab+b^2=(a-b)^2

y/3+3^2=(x-3)^2+26/3

▼

Solve for y

CalcPow

Calculate power

y/3+9=(x-3)^2+26/3

SubEqn

LHS-9=RHS-9

y/3=(x-3)^2+26/3-9

MultEqn

LHS * 3=RHS* 3

y=3(x-3)^2+26-27

SubTerm

Subtract term

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

Now we can identify the vertex. Graphing Form:& y=3(x- 3)^2+( - 1) Vertex:& ( 3, - 1) Notice that the axis of symmetry is a vertical line through a parabola's vertex. Therefore, the axis of symmetry must be x=3.

Again, when we complete the square the coefficient to x^2 has to be 1. Therefore, before we complete the square, we should first divide both sides by 3.

y=3x^2-4x-11 ⇓ y/3=x^2-4/3x-11/3Now we can complete the square by adding the square of half the coefficient to x to both sides of the equation.

y/3=x^2-4/3x-11/3

AddEqn

LHS+(-4/3/2)^2=RHS+(-4/3/2)^2

y/3+(-4/3/2)^2=x^2-4/3x+11/3-(-4/3/2)^2

▼

Simplify

NegBaseToPosBase

(- a)^2=a^2

y/3+(4/3/2)^2=x^2-4/3x-11/3+(4/3/2)^2

DivFracD

a/c/b= a/b* c

y/3+(4/6)^2=x^2-4/3x-11/3+(4/6)^2

CommutativePropAdd

Commutative Property of Addition

y/3+(4/6)^2=x^2-4/3x+(4/6)^2-11/3

SplitIntoFactors

Split into factors

y/3+(4/6)^2=x^2-2x(4/6)+(4/6)^2-11/3

FacNegPerfectSquare

a^2-2ab+b^2=(a-b)^2

y/3+(4/6)^2=(x-4/6)^2-11/3

▼

Solve for y

ReduceFrac

a/b=.a /2./.b /2.

y/3+(2/3)^2=(x-2/3)^2-11/3

PowQuot

(a/b)^m=a^m/b^m

y/3+4/9=(x-2/3)^2-11/3

SubEqn

LHS-4/9=RHS-4/9

y/3=(x-2/3)^2-11/3-4/9

ExpandFrac

a/b=a * 3/b * 3

y/3=(x-2/3)^2-33/9-4/9

MoveNegFracToNum

Put minus sign in numerator

y/3=(x-2/3)^2+- 33/9-4/9

SubFrac

Subtract fractions

y/3=(x-2/3)^2+- 37/9

MultEqn

LHS * 3=RHS* 3

y/3=(x-2/3)^2+- 37/9

MoveNegNumToFrac

Put minus sign in front of fraction

y=3(x-2/3)^2+(- 37/3)

Now we can identify the vertex correctly. Graphing Form:& y=3(x- 2/3)^2+( - 37/3) [1em] Vertex:& ( 2/3, - 37/3) Again, the axis of symmetry is a vertical line through a parabola's vertex. Therefore, the axis of symmetry must be x= 23.