Week 9 : Equivalent forms

This week we learned about equivalent forms.

So In short this chapter.

We learned 3 form to write quadratic function :

First one : General form : y=ax^2+bx+c

Second one : Standard form : y=a(x-q)^2+p

And the last one : Factored form : y=a(x-x1)(x-x2)

Cause factored form is new one we just learned so i will introduce little bit about it.

Let’s start with example :

And beside how can we change from the general from to factored or standard from. I will show you right now.

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

Let’s start with example :

Factor : x^2+12x+36

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


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 :


We knew : a=2

We will apply this formula :

Week 5 : Factoring Polynomials

This week we start to learn the new unit. That’s factoring polynomial expressions
Let’s star with the first example :

If the leading coefficient is 1 like this. The process to do this exercise is so easy. The only two numbers have sum is −4 and that multiply them to give −12 are −6 and 2. So if you wanna find the number have sum = -4 from -12 you can try by this way :

So right now we will chosse one into them. Which ones will help us get -4. That’s -6 and 2 ( -6+2=4 ).

So let’s try with another example :


It has a leading coefficient of 1, find two numbers with a product of 24 and a sum of −10.

Same as above exercise we will try each number multiply to get 24


Which one will help us get 10. Thats last. 4+6

Then we will get x^2-4x-6x+24. So we got it!!!!

Example 3 : 2x^2+9x-5

This example diffirent with two example exercise cause the leading coefficient is not 1 (x^2) . We still find two numbers, and those numbers will still add up to 9.


RIght? Cause 10x-1=9x. Its same but i change it to be easy to a simpler equation

Then we will distribute them together then get :


Between 2x^2+10x the same point is 2x then we will divide each number for 2x to get (x+5)

Same way with -1(x+5)

Finally we will make it simpler by the way, they have same (x+5). We will make the general figures between them.