Question

Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. y = x^2 + 2x + 1 and y = x^2 + 3x + 2

Answer 1

y=(x+1)(x+1)
y=(x+2)(x+1)

Answer 2

teach me how you got that? :)

Answer 3

x^2+2x+1 is a trinomial. We know that trinomals come from multiplying two binomials.
Are you with me so far?

Answer 4

yuup

Answer 5

Do you know how to multiply two binomials?

Answer 6

no... please do explain haha read my username :P

Answer 7

Have you heard of FOIL?

Answer 8

yeah

Answer 9

You multiply two binomials by using FOIL which means you multiply the First terms of the two binomials. O stands for Outer which means to multiply the outer terms of the two binomials. I stands for Inner which means you multiply the inner terms of the two binomials. L stands for Last which means you multiply the Last terms of the two binomials.

Answer 10

okay... so what im a foiling?

Answer 11

So when you factor a trinomial, you reverse that procedure. You have to find the two binomials that were multiplied to get the trinomial. But if you know how to FOIL, then you can figure out what the two binomials are.

Answer 12

For example: If I want to find two binomials that will multiply together to get x^2+2x+1 I know they both have to start with x: (x )(x )

Answer 13

Because x times x is x^2

Answer 14

ok im following

Answer 15

If I want to get the 1 on the end, then it would have to be 1 times 1 or -1 times -1

Answer 16

(x+1)(x+1) or (x-1)(x-1)

Answer 17

Then I check out the Outer and Inner to see which one gives me +2x.

Answer 18

Clearly it is the (x+1)(x+1)

Answer 19

makes sense

Answer 20

So those are the factors of x^2+2x+1 because when I multiply (x+1)(x+1) using FOIL, I get x^2+2x+1

Answer 21

So if I wanted to factor x^2+3x+2 once again the two binomials would have to start with x: (x )(x )

Answer 22

How could I get +2 for the last term?

Answer 23

x + 2

Answer 24

I could get +2 for the last term by multiplying 2 times 1 or -2 times -1
Which choice should I make and why?

Answer 25

2 times 1 will get you positive 2

Answer 26

So will -2 times -1

Answer 27

so why would either be wrong?

Answer 28

Because only one of them will result in +3x for the Outer + the Inner

Answer 29

so you need the positive ones right?

Answer 30

Yes.

Answer 31

Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 3x + 2 different from y = x2 + 2x + 1?

Answer 32

the first one has two distinct roots. The second one had 1 double root.

Answer 33

thanks so much!!!