Question

Part 1:
Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. Show your work to receive full credit.

y = x2 + 3x + 2
y = x2 + 2x + 1

@phi Can you help? I'm not good with the Quadratic Equation

Answer 1

I think you should factor them.

look at the last number: +2
1) list all pairs of numbers that give you 2 when you multiply them together
in this case: 1,2 is the only pair
2) the + sign on the 2 means your "factors" will have the same sign.
3) look at the +3 in +3x the + means the largest of the factors will be +
4) from step 1, you know you have factor +2. from step 2, you know 1 is also +
so your factors are +1 and +3
5) from your list of step 1 with signs as given in step 4, pick the pair that add up to
+3 (this +3 comes from +3x term)

in this case, there is only 1 pair, and it adds to 3. so you found the factors

6) write down (x + 1)(x+2)

Answer 2

to solve, you need an equation. normally you solve for when y = 0
x^2 + 3x + 2 =0

if you factor (see above) you get
(x+1)(x+2)=0

if x= -1 you will get 0 or if x=-2 you get 0

you would find these numbers by saying
x+1=0
add -1 to both sides
x+1-1= 0-1
x= -1

and
x+2= 0
add -2 to both sides
x+2-2= 0-2
x= -2

Answer 3

for the 2nd equation
y = x^2 + 2x + 1

can you do step 1) list all pairs of numbers that give you 1 (the last number)

Answer 4

Wait, so the first one is just x=-2?

and the pairs are only 1, 1.

Answer 5

re-read the 2nd post more carefully. what does it say?

Answer 6

Ohh. (x+1)(x+2)=0

Answer 7

do you understand that has two different x values that "work" (make the equation true)

Answer 8

Yes, sorry. I got distracted because I am watching a movie.

Answer 9

if x= -1 in (x+1)(x+2)=0 you get
(-1+1)*(-1+2) = 0 or
0 * (1) = 0
0 = 0

Answer 10

Okay. What about the second one.

Answer 11

or the 2nd equation
y = x^2 + 2x + 1

can you do step 1) list all pairs of numbers that give you 1 (the last number)
you said 1,1

now step 2)
2) the + sign on the 1 (the last number) means your "factors" will have the same sign.

step 3
3) look at the +2 in +2x the + means the largest of the factors will be +

what are your factors (and what sign are they) ?

Answer 12

The factors are 1 and 1 right? o.o

Answer 13

and both are +

Answer 14

I'm a little confused.

Answer 15

you got step 1.

now step 2
in y = x^2 + 2x + 1
look at the last number +1

the + sign means your factors will have the same sign (either both will be + or both -)

(if you had -1, it would mean the factors had opposite signs)

in this case, your factors will have the same sign. Which sign ?

step 3:
look at the middle term in
y = x^2 + 2x + 1

the + in +2x means the largest factor is +.

in your case, with 1,1 pick the first 1, and say it is +1

from step 2, you know both factors have the same sign. if you have a +1 the other factor (the other 1) is also +

so your factors are +1, +1

Answer 16

when you get to a boring spot in the movie, you can read that over until it makes sense

Answer 17

step 4 was figure out the signs: +1, and +1

step 5, from your list of pairs (in this case there is only 1 pair)
pick the pair that when added together give you the middle number in
x^2 + 2x + 1

you want the pair that add up to +2 (from +2x)
in your case +1 + 1 =2
so those are your factors

Answer 18

Okay, just so I can process this better to put it in answer form, can you help me shorten that up, so I can type it out > _ <

Answer 19

nobody types in that much. that is for you to go over when or if you want to learn how to do it. when people "show work" they write : "factor the quadratic into ...." and write
down the factored form (as if it were totally obvious to the most casual observer)

Answer 20

I just needed to find a shorter way to show my work. >_<

Answer 21

But my brain can't process all of the typing into a few sentences.