# Quadratic relations

### By.Prabhjeet

## Expanding

solving expanding quadratic equations is easy if you use the distributive property to expand binomials. Collect like terms to simplify.

example 1 : ( x + 4 ) ( x – 2 )

= x2 – 2x + 4x – 8= x2 + 2x – 8

example 2: ( x + 5 )2

= ( x + 5 ) ( x + 5 )

= x2 + 10x + 25

example 3 :( x – 3 ) ( x + 3 )

= x2 – 3x + 3x – 9= x2 – 9

## Factoring

Factoring is the opposite of expanding. If every term of a polynomial is divisible by the same constant, the constant is called a common factor. A polynomial is not considered to be completely factored until the greatest common factor (G.C.F. ) has been factored out.

For factoring with trinomials you just have to find two numbers whose product should give you C and added those numbers should give you B. factoring trinomial form is

Standard Form:__ a x^2+ bx + c__

example: x*^2-5X+6*

* x**^2-3x-2x+6*

* x(x-3)-2(x-3*

* (x-3)(x-2)*

example: 2y*^2-2y-60*

*2(y**^2-y-30)*

*2(y**^2-6y+5y-30)*

*2[y(y-6)+5(y-6)]*

*2(y-6)(y+5)*

*Factoring when a is not 1 is simple all you have to do is *

1: Multiple a by c

2: Find factors of new number

(find two numbers multiplied together to get c and added together to get b)

3: Write in standard form, using the original a and c value

4: Group and find common factors

5: Place in factor form: (x ) (x )

example:

3x*^2-8x+5*

*3x**^2-5x-3x+5*

*x(3x-5)-1(3x-5)*

*(3x-5)(x-1)*

## solving

## solving x-intercepts/roots

## word problem example

*^2+2x+3.*

*when does the driver hit the water?*

0=x*^2+2x-3*

*=(x-3)(x+1) *

*0=(x-3)=3*

*0=(x+1)=-1*

*therefore 3m *

## complete the square

*complete the square is when we take ax^2+bx+c=0 and turn it into a(x+d)^2+e=0.* *Completing the square is often used to figure out a vertex of a parabola.*

*example: 3x**^2+12x+13 *

* 3(x**^2+4x)+13*

* 3(x**^2+4x+2**^2-2**^2)+13*

* 3(x**^2+4x+2**^2)-3(4)+13*

* 3(x+2)-12+13*

* 3(x+2)**^2+1*

*Block out the first 2 terms*- Factor out the "a" value (which comes from standard form which we talked about earlier)
*Take half of the**x*-term coefficient and square it.- keep the positive number and take out the negative from the bracket
- Middle value is divided by 2 and then the entire bracket is squared.