Quadratic Relations Lesson

By: Cindy Cheng

A table of values represents a quadratic relation ie. for constant increments of the independent variable (x), the first differences (△y) are variable and the second differences [△(△y)] of the dependent variable (y) are constant.
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Common 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



_ _ _ _ _ _ _ _ _ _> common factor


  • a polynomial is not considered to be completely factored until the greatest common factor (G.C.F) has been factored out


4x+20=2(2x+10) → not completely factored

4x+20=4(x+5) → completely factored

Try it out:

a) 3x+9



Factoring By Grouping


bracket off first 2 and last 2 terms


factor the brackets


since (x+2) is the same, you can bring it together


Factoring by Grouping

Factoring Simple Trinomials


find two numbers that multiplies into 6 and adds to 7



the 2 numbers are 6 and 1.


Factoring Complex Trinomials


nothing that multiplies to -5 and adds to 3. So you have to multiply a(2) with c(-5) which would be your third term

P: -10

S: 3

decompose the middle term


factor by grouping



Factoring Difference of squares


if both terms can be squared and the second term is a negative, it can easily be factored.


solving quadratic equations by factoring


factor off the equation


there will be 2 answers that equal x in the end.

x+1=0 and x+2=0

x=-1 and x=-2

completing the square


block off the first 2 terms


factor out the A


add "zero" inside the brackets. To get zero-- (middle term/2)²


bring out the negative



factor the rest


Completing the Square - Solving Quadratic Equations

quadratic formula

formula you need to remember:

x2 + 3x – 4 = 0




plug into the formula and answer. you will get 2 answers.

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Using the Quadratic Formula

The End