# Week 8 : Properties of Quadratic Functions

This week we started with new lesson : Graphing Quadraction Functions about the determine the value of vertex, formula, what the graph looks like and how to draw the parabola.

So let’s start the things I studies in this week :

$y=ax^2+bx+c$ : It is general form of quadratic
With a (coefficent) it will helps us know the graph will be big or small.

Also, we can know : If quadratic positive $y=x^2$ , the parabola will be go up (+) and contrast if quadratic negative $y=-x^2$ , the parabola will go down.

It will be like this in graphing:

Vertex : highest and lowest point (-1,4)

Axis of Symmetry : which the parabola is symmetric (-1) of above picture

x-intercepts : zero of function or we can determine it by Quadractic Formula

y-intercepts : it depends on c

Maximum point : when the graph opens down Because the intersection point between x and y is at the top

Minimum point : when the graph opens up so the intersection point between x and y is at the bottom

Pattern of Parent Function :

$y=x^2$ it will show stretch / compress : 1,3,5,7,9..

But if $y=2x^2$ the stretch / compress : 2,4,6,10..

Domain : the value of x and the complete set of possible values of the independent variable, make sure it is real number.

Range : the value of y

$(x-p)^2$ : depends on the value of p, It will move to right or left

Let’s star with example :

$(x+7)^2$ : when p is positive the vertex move to left
$(x-7)^2$ : when p is negative the verter move to right

# Week 6 : Perfect square trinomials – The quadratic formula

Today, we will start with perfect square trinomials and The quadratic Formula

First : Perfect Square Trinomials
I will help you know more about that with first example :

We have already discussed perfect square trinomials:

$(a+b)^2= a^2+2ab+b^2$
$(a-b)^2= a^2-2ab+b^2$

We know : $a^2$ : Square of first term of binomial
2ab : twice the product of binomial’s first and last terms
$b^2$ : Square of last term of binomial

Factor : $x^2+12x+36$

Like my way, i always try the last term the numbers multiply together to get it like this :

36×1
18×2
12×3
9×4
6×6

I will choose 6×6 because if they multiply together, i will get 36 and when they add together, i will get 12 like the exercise i gave above.

You can do it faster than my way with perfect square.

Answer: (x+6)(x+6) or $(x+6)$

Example 2 : $9x^2-6x+1$

The leading coefficient is not 1 ($x^2$). Its 9 but Both $9x^2$ and 1 are perfect squares, and 6x is twice the product of 3x and 1.

So we will know a = 3a and b = 1.

Then get the answer : $(3x-1)^2$ or (3x-1)(3x-1)

Quadratic Formula : We will use this formula when we can not use Factoring and Binomial with complicated exercise. This formula will help us get answer easier and faster.

$x(1) = (-b+-(b^2-4ac)\div(2a)$
And now let’s start :

$2x^2+6x+9=0$

We knew : a=2
b=6
c=9

We will apply this formula :