Algebra Flashcards
What is Vertex Form/ Completing the Square?
y= a (x-h) 2+k
Example: y= (x+3) 2-1
What is* Standard Form?*
ax+by+c=0
Example: 2x-3y+7=0
*a is always positive
What is slope y-intercept form?
y=mx+b
Example: y= 2/3x+4
How do you turn an equation in standard form to y=mx+b?
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
How do you turn an equation in y=mx+b form to standard form?
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*
What is a Binomial?
An algebraic expression that contains 2 terms
What is a Monomial?
An algebraic expression that contains only 1 term
What is a Polynomial?
Another Name for an algebraic expression
What is a Trinomial?
An algebraic expression that contains three terms
What is Combining Like Terms/ Simplifying?
Combining terms with the same variable
What is Distributive Property or FOIL?
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
How do you square a binomial?
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
What is a Difference of Squares?
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
What is the Greatest Common Factor?
The biggest factor a group of numbers has in common.
Example: 15 and 25
GCF= 5
How do you Factor?
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)
How do you factor a Complex Trinomial?
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)
How do you factor a complex trinomial using Trial and Error?
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)
How do you factor a Perfect Square Trinomial?
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
How do you factor a Difference of Squares?
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)
Without solving, how to you show that a point is a solution to a system of equations?
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
What is Factoring By Grouping?
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)
How do you solve using Decomposition?
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)
How do you solve using theTrial and Error Method?
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)
How do you find the value of C/ Completing the Square
Divide the b term by 2 and square it
What value(s) of c make the expression x2-18x+x a perfect square?
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
Write in standard form
a) 5x-7y=35
b) 9x= 54-6y
a) 5x-7y-35=0
b) 9x+6y-54=0
What value(s) of b make the expression x2+bx+25 a perfect square?
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
