# QUADRATICS

### Learn more about quadratics

## Multiplying Binomials

-> When muliplying binomials always remember FOIL

F- stands for first

O- stands for outer

I- stands for inner

L- stands for last

Example: (x+2) (x+3)

1st step: (x+2) (x+3) "x" muitiplied by "x" = x squared

(First)

2nd step: (x+2) (x+3) "x" multiplied by 3 = 3x

(outer)

3rd step: (x+2) (x+3) 2 multiplied by "x"= 2x

(inner)

4th step: (x+2) (x+3) 2 mulitlplied by 3 = 6

(last)

Rewrite: xsquared + 3x + 2x + 6

collect like terms: xsquared + 5x + 6

^ this now is a simple trinomial

* keep reading down and learn how to solve simple trinomials*

## Common Factoring

NOTE: Common factoring is the opposite of expanding

-> An example is given below which step by step shows you how to solve for common factoring.

Ex: 10x+5

1st: find GCF for 10 and 5

10- 1,2,5 and 10

5- 1 and 5

GCF: 5

2nd: Write soultion with brackets but first divide GCF number 5 with 10x+5

10x/5 + 5/5

- GCF goes on the outside of brackets

5(2x+1)

Lastly check answer

5(2x+1) = 10x+5

## Factor Simple Quadratic Expressions of the Form x^ + bx + c

NOTE: When factoring a polynomial of the form of x^ + bx + c (when a=1) we should find the:

- two numbers that add to give b

- two numbers that multiply to give c

-> to help you understand this expression completely always write x^ + bx + c before solving

Here is an example: x^ + 5x + 6

x^ + bx + c

- before doing anything find the sum and product 2 multiplied by 3 = 6 / 2 plus 3 = 6

Therefore the answer is (x+2) (x+3)

## Factor complex quadratic expressions of the form ax^ + bx + c

-Here is an example on how to solve for complex trinomials

-There will also be a video after the example, if you still haven't fully understood the concepts to complex trinomials

Example: 3x^ + 8x + 5

ax^ + bx + c <- rewrite the formula

3x^ + 8x + 5 <- multiply the "a" with "c"

product: 3 times 5 = 15

sum: 3+5=8

-Factor by grouping:

(3x^ + 3x) (5x + 5)

= 3x(x+1) + 5(x+1)

- now write (x+1) (3x+5) <- this is the final answer for now

NOTE: The video below shows another method, you can chose whatever method suits you they both give you the same answers.

## Factor a perfect square trinomial

-Here is easy example of a perfect square

- Afterwards watch a video that is a bit more complex step by step

Example: Expand and simplify this: (x +4)^

(x + 4)^

=(x+4) (x+4)

- Before doing anything remember FOIL

-Use FOIL to simplify

First: x time x

Outer: x times 4

Inner: 4 times x

Last: 4 times 4

= x^ + 4x + 4x + 16

- Now collect like terms which are (4x,4x) add these terms together

= x^ + 8x +16

## Factor differences of square

Example: 9k^-25=0 (differences of squares)

(3k+5) (3k-5)=0

(3k+5)=0

3k divide 3 and 5 divide 3

k=5 over 3

(3k-5)=0

3k divide 3 and -5 divide 3

k= -5 over 3

## maxima and minima

- The difference between max and a min is that a max will have an negative in front of the "a" value and the min would be positive which means that it can go further up

Example of a Maxima: y=-x^ + 8x - 3

Example of Minima: y=x^ + 4x - 3

## Transformations

-label each property, so it's easy to know what is what

- here is an example below

- draw chart for organization

PROPERTIES/ Y (X+3)^

-vertex/ (-3,0)

-A.O.S/ x=-3

-stretch or compression/ none

-direction of opening/ upward

-value x may take/ set of real numbers

-Value of y may take/ y=-3

## word problems

Now its getting harder, now there is a word problem and you have to solve it by using any quadratic equation or formula.

- remember highlighting or underling important things in word problems helps a lot

The word problem is:

## graphing parabolas in y=a(x-h)^+k form

- I will be teaching how to find the y and x vertex by taking turns and letting x=0 and y=0

- also then teaching how you can use the square root or quadratic formula to solve

- then graphing the parabola

## the quadratic formula

- quadratic equations that can be factored are really easy to solve but those quadratic equations that cannot be solved there is a formula for them

Formula:

x= -b-+ square root (b^-4ac)

divided by 2a

-Sorry guys I did do my video but its taking forever for it to upload so I couldn't post it