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 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 :

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 :