Algebra

Question 1

What is Vertex Form/ Completing the Square?

Answer 1

y= a (x-h) ²+k

Example: y= (x+3) ²-1

Question 2

What is* Standard Form?*

Answer 2

ax+by+c=0

Example: 2x-3y+7=0

*a is always positive

Question 3

What is slope y-intercept form?

Answer 3

y=mx+b

Example: y= 2/3x+4

Question 4

How do you turn an equation in standard form to y=mx+b?

Answer 4

Rearrange the equation and isolate y

Example: x+3y+9=0 3y= -x-9

*Divide each term by 3 to isolate y

y= -1/3x-3

Question 5

How do you turn an equation in y=mx+b form to standard form?

Answer 5

Example: y= 2x-3

Step 1) Move all terms to the left side *Electric Fence

-2x+y+3=0

Step 2) Get rid of any fractions or decimals

Step 3) Ensure A is positive (x-1)

2x-y-3=0

*Remember the equation should go X- Y - Number*

Question 6

What is a Binomial?

Answer 6

An algebraic expression that contains 2 terms

Question 7

What is a Monomial?

Answer 7

An algebraic expression that contains only 1 term

Question 8

What is a Polynomial?

Answer 8

Another Name for an algebraic expression

Question 9

What is a Trinomial?

Answer 9

An algebraic expression that contains three terms

Question 10

What is Combining Like Terms/ Simplifying?

Answer 10

Combining terms with the same variable

Question 11

What is Distributive Property or FOIL?

Answer 11

A method used when multiplying monomials and polynomials. You Multiply everything outside of the brackets by what is inside the brackets OR multiply 2 sets of brackets by eachother

Example: 5 (3x-2) =15x-10

Question 12

How do you square a binomial?

Answer 12

Example: (x+1)²

Step 1) Write the binomial twice

(x+1) (x+1)

Step 2) Use the distributive property

x²+x+x+1

Step 3) Group Like Terms

x²+2x+1

Question 13

What is a Difference of Squares?

Answer 13

The product when you multiply the sum and difference of 2 terms, the middle terms add to 0.

Example: (a+b) (a-b)= a²- b²

Question 14

What is the Greatest Common Factor?

Answer 14

The biggest factor a group of numbers has in common.

Example: 15 and 25

GCF= 5

Question 15

How do you Factor?

Answer 15

Example: 2x+2

Step 1) Take away the greatest common factor from all the terms in the equation

GCF=2

2x/2+2/2

Step 2) Take the number you factored out and put it outside of brackets, with the remainder of the equation in brackets

2 (x+1)

Question 16

How do you factor a Complex Trinomial?

Answer 16

Example: 3x²+5x+2

Step 1) Check for common factors

P= 6 (2x3)

S= 5

Step 2) Find 2 integers with the sum of 5 and the product of 6

2 and 3

Step 3) Decompose by using the 2 intergers . Then factor by grouping.

3x²+2x+3x+2

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

Question 17

How do you factor a complex trinomial using Trial and Error?

Answer 17

Example: 2x²+11x+12

Step 1) Check for common factors

S= 11

P= 24

Step 2) Trials- List out factors of 2 and 12 and multiply in a cross pattern. Try until you get a sum of 11

2 3

1 4

Step 3) Write out the equation

(2x+3) (x+4)

Question 18

How do you factor a Perfect Square Trinomial?

Answer 18

Example: x²+14x+49

Step 1) Check for common factors

S= 14

P= 49

Step 2) Reconize that the 1st and 3rd terms of the trinomial are perfect squares. Check if the middle term is twice the product of the 1st and the 3rd terms

(x+7) (x+7)

Step 3)Write in the form (a+b) ²

(x+7) ²

Question 19

How do you factor a Difference of Squares?

Answer 19

Example: x²-49

Step 1) Check for common factors

Step 2) Recognize that both terms are perfect squares and that it is a difference, not a sum

Step 3) Write in the form (a+b) (a-b)

(x+7) (x-7)

Question 20

Without solving, how to you show that a point is a solution to a system of equations?

Answer 20

Using a table of values place the eqation and its answer on each side and replace the ordered pair into the x and y variable places. Show that both sides are equal.

Example: (-2, -5)

3x-4y **14 **

3(-2) -4 (-5)

-6+20

14

Question 21

What is Factoring By Grouping?

Answer 21

Grouping together terms in an equation that have something in common, and factoring it out.

Example: 9x²+ 15x -3x-5

Groups: 9x² and -3x ; 15x and -5

3x(3x-1) + 5(3x-1)

(3x-1) (3x+5)

Question 22

How do you solve using Decomposition?

Answer 22

Example: 10x²-x-2

Step 1) Find the sum and product of the equation

S= -1

P=20

Step 2) Write out the equation using the 2 new numbers

10x²+4x-5x-2

Step 3) Factor by grouping

10x² and -5x ; 4x and -2

5x(2x-1) 2(2x-1)

Step 4) Take the repeated term in brackets and whats outside of the brackets and make them 2 new terms

(2x-1) (5x+2)

Question 23

How do you solve using theTrial and Error Method?

Answer 23

Example: 6x²-13x-5

Step 1) Write out 2 factors of each number in the equation

2 1

3 -5

Step 2) Try different combinations of numbers until when cross multiplied, they add to the middle number

3 x -5 = -15

2 x 1 = 2

-15 + 2 = -13

Step 3) Write in factored form, going horizontally

(3x+1) (2x-5)

Question 24

How do you find the value of C/ Completing the Square

Answer 24

Divide the b term by 2 and square it

Question 25

What value(s) of c make the expression x²-18x+x a perfect square?

Answer 25

Step 1) Divide -18x by 2

-18x/2

Step 2) Take the product and square it

19²

Step 3) The product from step 2 is the value of c

c=81

Question 26

Write in standard form

a) 5x-7y=35
b) 9x= 54-6y

Answer 26

a) 5x-7y-35=0
b) 9x+6y-54=0

Question 27

What value(s) of b make the expression x²+bx+25 a perfect square?

Answer 27

Step 1) Factor 25

(x+5) (x+5)

Step 2) Add together the numbers in step 1

5+5=10

Step 3) The answer from step 2 is the value of b

b=10