Alright what we are going to do is look at a function like this.
I want to show you the relationship between the function and it’s graph.
If you create a t-table and you plot this parabola you get this graph over here.
You can find the vertex, by the vertex formula…that’s how I got the (2,-15), but how do we get the two x-intercepts where y is 0.
Let y=0, we get this equation.  
We are supposed to solve this.
There are 3 ways to solve it.
The first way is to solve by Factoring.
The second way is by Completing the Square which is kinda tough but leads into the third way.
The third way is by the Quadratic Formula.
The quadratic formula will solve ANY quadratic.  
Quadratic is Degree 2 – Any function with highest exponent on the x is a 2 – the quadratic formula will solve it.
So what we are looking here is when y = 0 which is the x-intercepts of the parabola.
An example here.
Solve this equation and find the two answers that make this equal to zero.
This is a trinomial so it must factor into two binomials.
What two numbers multiply to -12 but add to -4.
-6 and +2
Now we are using the zero-product theorem which says (x+2) times (x-6) equals zero.
So either (x+2) is a zero or the (x-6) is a zero.
What x creates this zero.  Solve both.
X=-2  or X=6
So if I check -2 into the equation I should get zero!
(I make a small mistake but I fix it, I put a 2 instead of -2 in)    4+8-12  = 0
So if I do the same with 6 you should get zero also.  You should try it!
That’s the factoring technique.  The answers are -2 and 6.
Let’s go back up to the parabola and look at the x-intercepts of this function.
-2 produces 0  and 6 produces 0.
Let’s look at completing the square.
Same equation here.
Complete square only on first two terms, so get rid of -12 by adding 12 to both sides.
Then take HALF of the middle coefficient, and then square it and add it to both sides.
(-4/2)^2 = 4   Add 4 to both sides.
Now factor the left side – it’s a square binomial.
It’s always half of the middle coefficient – so  -4/2 = -2   so we have (x-2)^2
Then square root both sides, remember the plus or minus on the right side.
So I get  x-2 = + - 4
That is two different equations:  x-2 = 4   and x-2 =-4   solve them.
X=6 and x = -2
That’s getting the same two answers, but by completing the square.  
I would rather factor this problem instead of completing the square, but that’s how you do it.
Now the quadratic formula is the third way.
It will solve ANY quadratic equation.
I have it set equal to zero and then find my a, b, and c.  
Then fill in the numbers into the formula and calculate.
Start inside radical first and do the order of operations.
Two answers again:  (4+8)/2  = 6    (4-8)/2 = -2
Same two answers.
You can use any method to solve a quadratic equation.  
It all depends on how it’s set up.  
This one is set up to use factoring, because it factors easily.
But you can use any method.
The quadratic formula always works and the completing the square always works, but factoring won’t always work.
What you are doing when you’re solving these equations, is that you are basically finding the numbers that make it equal to zero which are 
the x-intercepts of the function form when graphed. 
Hope that helps.
