Completing the square/factors

From Math Wiki

x^2 + 6x + 8 = y

• To find the factor terms first look to see what numbers can be multipied to equal 8

1,2,4,8

• Next look to see which of those factors would add up to 6

2 + 4

• Then put in binomial form

(x + 2)(x + 4)

Now if you are supposed to graph it you can start out by looking at these numbers above which are also known as factored form, and start out by figuring well what from 2 will get me 0 and what from 4 will get me back down to 0. The answer would be -2 and -4. This is how you can start out graphing because these points are known as the "roots." Roots are the numbers taking from factored form and placed on the x-axis line. So when graphing, you will make 2 points one dot on the -2 and the other on the -4 so start off your graph!

• To put it in vertex form, first you need to split the 6 in half and put it in binomial form that way

(x+3)(x+3)

• Then you can simplify it

(x+3)^2

-but because 3^2 equals 9, not the 8 in the original problem, so you need to make them equal.

• To make them equal you add a number on to the end that will make the numbers work out. In this problem you add a -1 because 9-1 gives you the 8 that is in the original problem

(x+3)^2 -1

• If you distribute that out again you'll find that it equals the original problem exactly

(x+3)(x+3)-1

x^2 +3x +3x +9 -1

x^2 +6x +8

• If you'd futhermore like to brake down the equation to where you'd first multiply these binomial terms you would simply do the Distributive Property. Heres 5 easys steps to multiply the binomial terms above. (x + 2) (x + 4)

Step 1: Taking, x and multiplying it by x, you get x squared. x²

Step 2: Next you multiply x by 4, thus you now have 4x.

Step 3: You would do the same for 2. You'd multiply 2 by x giving you 2x.

And then 2 by 4 giving you 8.

Step 4: "Heres what we have so far": x²+4x+2x+8

Step 5: For the last step ALL you have to do is add like terms....so 4x plus 2x equals 6x.

And your final equation or answer is: _y=x²+6x+8