## Step Pattern

A step Pattern is something we use to the next points in a parabolas

A parabolas without "A" in it's equation, step pattern will always be over 1, up 1 and over 2, up 4

## Vertex Form

Y=A(X+H)^2+K

H equal to the x-axis of the vertex and the axis of symmetry

K equal to the y-axis of the vertex and the Optimal Value.

A multiples the y-axis in step pattern and if A is negative, the parabolas will open downwards and if A is positive, the parabolas will open upwards

## Standard or Trinomial Form

Y=AX^2 + BX + C

C is the same as y-intercept

A multiples the y-axis in step pattern and if A is negative, the parabolas will open downwards and if A is positive, the parabolas will open upwards

## Binomials or factored Form

Y=A(X+H)(X+K)

H & K are the 2 x-intercepts

X equal to the x-axis of the vertex and the axis of symmetry

Y equal to the y-axis of the vertex and the Optimal Value

A value only change the Optimal Value

• Linear Relationships have equal 1st differences
• Quadratic Relationships have equal 2nd differences

## Multiplying Common Binomials or changing factored form to standard form

There are 3 ways to multiply Common Binomials

## Factoring by Grouping

In order to factor binomial with 4 terms you must factor it in pairs

AX+BX+CX+DX

1. take the 1st 2 terms and factor them
2. do the same with the 3rd and 4th terms

## Factoring Simple Trinomials or changing standard form to factored form

Simple are Trinomials with a coff of 1.

Ex.X+BX+C

To factor trinomials you must remember this rules

X is always X^2

C is equal to two of it's factors

B is the sum of C's factors

see Picture for Examples

## Factoring Complex Trinomials

Complex Trinomials are Trinomials wih a coff more than 1

Ex.AX+BX+C

To factor this you must change to a simple Trinomial by find the GCF of A, B, and C

If there is no GCF than use the Trial and Error to find answer

see Picture for Examples

## Factoring Perfect Squares

Perfect Squares are Binomials where R and S are the same number

(X-R)^2=(X-S)(X-R)

To factor this you could factor as if it was common binomials or

1. squares X.

2. times X and R together than times by 2.

3. Squares R.

see Picture for Examples

## Factoring Difference of squares

Difference of squares is difference of perfect squares (if you take the square root, it is a whole number) Ex.1,4,9,16,25,36,49,64,81,100...

X^2-R=(X-R)(X+R)

To factor this is

1. find square root of X and R.

2. then to it together one negative and one positive

See Picture for Example

## Solving Quadratic equations by factoring or Finding X-intercepts from standard form

1. always sub:Y=0
2. factor the equation
3. isolate X
4. solve by Elimination
5. Check for work

## Completing the square or changing standard form(AX^2+BX+C) to vertex form(A(X-B)^2+C)

1. divide B by A then take x^2+bx in a bracket and leave c alone = y=A(X^2+BX)+C
2. divide b by 2 then square it by 2 = (B/2)^2
3. put the total with x^2+bx = A(X^2+B+D)+C
4. subtract or add D to rid of it = A(X^2+B+D+/-F)+C
5. factor X^2+B+D then times A with F and then take the total out of the bracket = A(X+B)^2+/-F+C
6. add or subtract F and C = A(X-B)^2+C