Quadratic Relations

Rushan Niazi - MPM 2D0-G

Topics

1. Multiplying Binomials (Expanding)

2. Factoring

3. Solving

- Completing the Square

4. Quadratic Formula

5. Properties of a Parabola

Quadratic Relations

A table of values represents a quadratic relation if for the constant increments of independent variable (x), 1st differences, are variable and the 2nd differences of the dependent (y) variable are constant.


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

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

Multiplying Binomials

The FOIL Method - Multiplying Binomials - MathHelp.com

Common Factoring

Common factoring is the opposite of expanding:

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)

Big image

Factor by Grouping

ax-bx-ay+by

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

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

=(a-b)(x-y)

Solving an Equation: Factoring Simple and Complex Trinomials

Solve a Quadratic by Factoring - Simple Trinomial and Complex Trinomial

Factoring Difference of Square

When an equation is in this form:

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

x^2+6x-2

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

Big image

Quadratic Formula

Quadratic Formula 1

Properties of Quadratic Relations

The graph of a quadratic is called a PARABOLA

- 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)

Big image