Question

Can someone help me to function f(x) = 2x2 + 4x – 6

Answer 1

bump

Answer 2

What do you need? Do you need to factor it or find the solutions ?

Answer 3

Yep! I have to factor it

Answer 4

I was looking through my lesson book and they showed the steps but I still couldnt quite get it

Answer 5

I think a 1 will be involved but Im not sure how

Answer 6

Sorry I am at work so I am in and out.

\( ax^2 + bx + c\)

That is the normal form above.

Yours is
\( 2x^2 + 4x - 6\)

Can you tell me what number is a and b and c in \( 2x^2 + 4x - 6\)?

Answer 7

Ok, a is 2

b is 4

and 6 is c

Answer 8

\( 2x^2 + 4x - 6\)

Take a and times it by c, you get 12. Now what two numbers gives you the sum of b,which is 4? The number 6 and - 2 will give you the sum of 4. 6 + -2 = +4, which 4 is out b number.

Now put those two numbers in the quadratic like below to make up our b and then factor by grouping.

\( 2x^2 + 6x + -2x - 6\)

Let me know if you understand what I am doing here.

Answer 9

How did you get -2?

Answer 10

I times a and b, which is 2 * 6, which gave me 12. Then I took 2 and 6 and looked to see how they will equal 4. Do you see that?

Answer 11

Ohhhh making it 6-2 giving it a -2

Answer 12

Yes correct

Answer 13

Oh okay

Answer 14

Now we have

\( \ 2x^2 + 6x + -2x - 6\)

We want to group and then find the factors
We will group and factor
\( 2x^2 + 6x \)

and then

\( -2x - 6\)

Answer 15

How come your subtracting instead of adding?

Answer 16

\( 2x^2 + 6x\)

What can we divide into this?

We can divide 2x into \(2x^2\) and into 6x
\( \frac{ 2x^2 + 6x}{2x} \)

2x(x + 3)

Now let do

\( -2x - 6\)

\( \frac{-2x - 6}{-2}\)

-2(x + 3)


Now we have
2x(x + 3)

and
-2(x + 3)

OR
2x(x + 3) -2(x + 3)

Now we need to factor out (x+3), which will give us

\( \frac{2x(x + 3) -2(x + 3)}{(x + 3)} \)

and then we have

(x+3) (2x -2)

And this is our factor (x+3) (2x -2) .


Now to find our solutions of the function, we set the factors to zero

x + 3 = 0
x = -3


2x - 2 = 0
2x = 2
x = 2/2
x = 1

So our solutions are x = -3 and x = 1

Answer 17

Also, what do you mean I am subtracting? I am adding.

Answer 18

I think i get it

Answer 19

Let me know if you have any questions. If you just want to factor, the answer is
(x+3) (2x -2)

If you need solutions, the answer is x = -3 and x = 1

Answer 20

ok, thank you!

Answer 21

YW, it takes time to wrap your head around it all but keep practicing at them and you will get them. The more you do them the easier they become. Also, if you have any questions feel free to ask.