# Quadratic Relations

### Rushan Niazi - MPM 2D0-G

## Topics

2. Factoring

3. Solving

- Completing the Square

4. Quadratic Formula

5. Properties of a Parabola

## Quadratic Relations

A polynomial of a degree of 2 models a quadratic relation:

EX. x^2, 3x^2-4x+5, x^2+1

## Multiplying Binomials

## Common Factoring

If every term of a polynomial is divisible by the same constant, the constant is called __common factor.__

ab+ac=a(b+c)------------------------------------------------------------> 4x+20=4(x+5)

## Factor by Grouping

=(ax-bx)(-ay+by)

=x(a-b)-y(a-b)

=(a-b)(x-y)

## Solving an Equation: Factoring Simple and Complex Trinomials

## Factoring Difference of Square

a^2-b

It can be factored very easily,

(a+b)(a-b)

this is called factoring difference of square.

x^2-4

=(x+2)(x-2)

you take the B term and square it (B=-4)

## Completing the Square

1. Block off first two terms (x^2+6x)-2

2. Factor out the A term

3.Add "zero" (B term/2 and then squared) (x^2+6x+9-9)-2

4.Bring out the negative (x^2+6x+9x)-9-2

=(x^2+3)-11

## Quadratic Formula

## Quadratic Formula

## Properties of Quadratic Relations

- Vertex = Point at which the parabola is at its highest or lowest

- A parabola is symmetrical from a axis of symmetry located in between the 2 zeros (x-intercepts)