Quadratic Relations

Rushan Niazi - MPM 2D0-G


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)

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Factor by Grouping





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:


It can be factored very easily,


this is called factoring difference of square.



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


Quadratic Formula

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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)

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