Remember: There is more than 1 way to do everything.

This is only one way. Whatever works for you.

__Quadratic formula__

1. Get the quadratic equation in standard form (ax^{2}+bx+c=0).

2.

3. Substitute for a,b, and c.

4. seperate into 2 equations (+ and -)

__Roots of a quadratic equation__

1. Get everything to 1 side (set =0)

2. Factor

3. Set each factor=0

4. Solve each equation for x.

5. Check your solutions.

__Factoring trinomial when a is not =1____ ____(Lesson 5)__

1-4. Same as when a=1

5. Rewrite original equation as ax^{2}+first(x)+second(x)+c

6. Pull out common factors of first two terms and last two terms.

7. Answer = (shared terms)(remaining terms.

Ex: 3x^{2}-x-4

3(-4)=-12 -12=-1(12), 1(-12), -2(6), 2(-6), 3(-4), -3(4)

-4+3=-1

3x^{2}+3x-4x-4

3x(x+1)+-4(x+1)

(x+1)(3x+4)

__Factoring trinomial with a=1____ ____(ax__^{2}__+bx+c)____ ____(Lesson 5)__

1. Multiply a(c)

2. Find all factor pairs of that number. (call them first and second)

3. Choose the pair whose SUM is b.

4. Factors are (x+first)(x+second) (minus if negative)

Ex: x^{2}-5x-14

1(-14)=-14 -14=-1(14), 1(-14), -2(7), or 2(-7)

-7+2=-5

(x+2)(x-7) = answer

__Common Factors: (Lesson 4)__

1. Write each part expanded to lowest form (ex 4x^{2}=2*2*x*x)

2. Everything that is shared circle (or underline)

3. Write Shared Terms(Leftover Terms)

Ex. 12x^{2}y+18xy^{2}

** 2***2*

*****

__3__***x***

__x__**+**

__y__*****

__2__***3***

__3__*****

__x__

__y__2*3*x*y(2*x+3*y) or 6xy(2x+3y)

__Difference of Perfect Squares: (Lesson 4)__

1. Take the square root of each part.

2. Answer is (square root of first + square root of second)(Square root of first - square root of second)

Ex. x^{2}-y^{2}^{ Factors to: (x+y)(x-y)}

__Solving Absolute Value Inequalities: (Lesson 3)__

1-5. Same as solving an equation (don't worry about sign yet)

6. If original question is < then "Thumbs Down."

Your solution will look like __smaller number < x < bigger number__

7. If original question is > then "Thumbs Up."

Your solution will look like __x __

__AND__

__x> bigger number__

__ __

__Solving Absolute Value Equations: (Lesson 2)__

__1. Get the absolute value by itself on one side__

__2. Once the absolute value is by itself, make sure it equals a positive number otherwise there are no solutions.__

__3. Set up 2 equations, 1 where it equals what it equals, the other where it equals the negative. ONLY negate the right side.__

__4. Solve for each equations using inverse operations. (addition<-->subtraction, multiplication<-->division)__

__5. There will be 2 solutions (unless = 0) __