Slope = Rise           
  Run

or

Slope =     y₂ – y₁    where  (x 1, y 1) and ( x2, y2) are
                    x₂ – x ₁         points  on the line.

Slope Intercept Formula

Y  = m x + b   where  m= slope  and  b is the y intercept   and (0,b) is the y intercept point

Point- Slope Formula

Y – Y₁ = m ( X – X₁)         

where  ( x₁, y₁)  is a point on  the line,  m is the slope

                  Area =  Side * Side

Perimeter of a trangle

Just add up the 3 sides.

Area of a Parallelogram= base * height

Perimeter of a Parallellogram

Just add up the 4 sides.

Area of a Trapezoid = 1 * (b1 + b2) h

            2

Perimeter of a Trapezoid

Just add up the 4 sides

Perimeter of a Circle

The Circumference

Circumference = diameter * pi

Area of a Semi Circle

( 1/2 of a circle)

Area of a Semi Circle  = 1 * pi* r²
                       2 

OR

Area of a Semi Circle  = 0.5 * pi* r²
                       

Difference of  2 Squares

a² - b² = ( a + b) ( a - b)

Example

x² - 9 = (x + 3) ( x - 3)

Difference of 2 Cubes

Sum of 2 Cubes

a³ + b³ = (a +b) (a² - ab + b²)

Example

x³ + 64 = x³ +4³ = ( x+4) (x² - 4x + 16)

AC Method for factoring

ax² + bx + c where a ≠0.

Factor   2x²+ 7x + 3

Steps

1)   Identify a, b, and c.

2)   Find two factors of ac that add to b.

3)   Split the middle term using the two factors you found.

4)   Factor by grouping.

Example

Factor   2x²+ 7x + 3

Step 1  a = 2, b = 7 c= 3

Step 2  ac = 2 * 3 = 6  b = 7

Factors of 6 are:     Sums of these factors.

     2 and 3                 2+3 = 5

     1 and 6                 1 + 6 =7

Step 3 Rewrite by splitting the middle term using the factors we found.

So 7x = 6x + 1  rewrite

2x²+ 7x + 3

2x² + 6x + 1x + 3

Step 4 Factor by grouping.

=2x² + 6x + 1x + 3

=2(x+3) +1(x + 3)

= (x+3) (2x + 1)  factored form.

Or (2x + 1) (x + 3)

Perfect Square Trinomial

a²+2ab+b² = (a+b)(a+b) =(a+b)²

^Factor

x²+ 10x+25 =

Perfect Square Trinomial

a²+2ab+b² = (a+b)(a+b) =(a+b)²

Example

x²+ 10x+25 = (x+5)(x+5) = (x+5)²

When factoring if you have

4 or more terms you would .. .

Factor by Grouping

Step 1 Pair up the 1^st 2 terms and the last 2 terms.

Step 2 Factor each pair.
Step 3 Then factor out the binomial.

Example

Factor  x² -3x + 2x - 6
          = x² -3x + 2x - 6

              = x( x-3) + 2( x-3)

          = (x -3) ( x + 2)

When factoring if you have

3 terms you would .. .

Use the AC Method to factor

or check for a Perfect Trinomial Square.

a²+2ab+b² = (a+b)(a+b) =(a+b)²

x²+ 10x+25=(x+5)(x+5) = (x+5)²

When factoring if you have

2 terms you would .. .

When factoring if you have

2 terms you would .. .

Check to see if you have one of the following:

Difference of 2 Squares

Difference of2 Cubes

Sum of 2 Cubes