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)