Question

Fanning + Medal Thank you
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.

0 = x2 + 5x + 6
0 = x2 + 4x + 4
Part 2:
Using complete sentences, answer the following questions about the two quadratic equations above.
Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 4x + 4 different from y = x2 + 5x + 6?

Answer 1

Can someone check if this is right?
X^2 + 5x + 6 = 0
this can be factorised as
X^2 + 2x + 3x + 6 = 0
X(x+2) + 3 ( x + 2) = 0
(x+2) * ( x + 3 ) = 0
x = -2 or -3

For x^2 + 4x + 4,
it is factorised as
x^2 + 2x + 2x + 4 =0
this simplifies to
(x+ 2) * (x+2) =0
or (x+2)^2 =0
in both cases, x = -2

Answer 2

@jdoe0001

Answer 3

Why are you doing a strange x? Also, if you put thinge between `\( \)` you can get math to come out nice. `\(x^2 + 5x + 6 = 0\)` becomes: \(x^2 + 5x + 6 = 0\)

Answer 4

My fault

Answer 5

First looks correct.... and so does the second.

I was just poinging out the \(\LaTeX\) so you can make thinks look nice. =)

Answer 6

So, do you see what they share in common?

Answer 7

Loll and yes they both equal x=-2

Answer 8

Yes, they share a sollution.
https://www.desmos.com/calculator/cyli9hnst3

But they are different because of what they do not share.

Answer 9

What is the link for? And I don't know why they're different from each other

Answer 10

The links shows it visually. That is the graph of those two equations. All you really need is the x axis, where they are 0.

Answer 11

If they share one solution, what about the other? How many unique solutions does each have?

Answer 12

@e.mccormick I'm not sure what this means?

Answer 13

I know that the first one already has 2 solutions

Answer 14

Well, a unique solution is a solution that is different. For one you got -2 and -3. For the other you got -2 and -2. So from a unique solutions viewpoint, the second has only one unique solution.

Your question says, "What makes y = x2 + 4x + 4 different from y = x2 + 5x + 6?" so you need to word that as part of an answer to that.

Answer 15

@e.mccormick so your basically explaining the part 2

Answer 16

Well, I am talking about how to answer part 2....

Answer 17

Wait now i'm confused

Answer 18

I am not going to write out, "Using complete sentences, answer the following questions about the two quadratic equations above." That is me answering your question. But I will gladly point out what you need to look at to find things that are similar and different.

Answer 19

alright

Answer 20

That i why I said you need to look at what they share, and you know that to be one answer, and what they do not share. However, it is not just the other answer that is not shared. Think about the number of unique answers.

Answer 21

My brother was helping me with this question but he had to go so now i'm all confused with what he was telling me

Answer 22

What did he tell you?

Answer 23

He told me all those things I put up there he's not the best explainer

Answer 24

So he was showing you the factoring by grouping to find the numeric part of the answer.

Answer 25

By numeric part I mean Part 1. Numeric means with numbers. Part 2 is words, so not numeric.

Answer 26

Oh ok but wait did I only show you the part 1

Answer 27

Yes, and what you put as correct. Which is why I moved on to part 2.

Answer 28

do you understand how the factor by grouping works?

Answer 29

I think

Answer 30

Can I tell you what I think for part 2

Answer 31

Sure!

Answer 32

Loll ok what makes the two equation so different is because the second equation is touching the x-axis when graphing, and the first equation is goes through the x - axis which gives it to x - intercepts

Answer 33

Am I right.Take your time reading it. And thanks for being patient with me when it comes to math it's very hard for me to comprehend

Answer 34

That is a good way to desribe it. Then, just add in what you know about the -2 solution.

Answer 35

Huh?

Answer 36

How will I be able to add it in

Answer 37

And what you say touching, you could add "and only has one solution." That makes it clear what you mean. \(\ddot \smile\)

Well, you have two questions to answer: same and different. It is for the same part.

Answer 38

:) I'm really happy with you because it's been an hour thanks and I definitely will add you.

Answer 39

As for factor by grouping, let me try an example that might help.

Sometimes the best way to start with these it to think back to numbers. Sure, they are silly examples at times, but they are also usually simpler and easier. Like if I said to factor something out of 6+10.

\(6+10 \implies 2\cdot 3+ 2\cdot 5\) Now they have a common factor.

When I group them I take that common factor out of both of them and put ( ) around:

\( 2\cdot 3+ 2\cdot 5 \implies 2( 3+ 5)\)

Now, that is the foundation, the very basic thing, that let your brother show you the first part.

Answer 40

And is that all I need now...what makes the two equation so different is because the second equation is touching the x-axis when graphing, and the first equation is goes through the x - axis which gives it to x - intercepts.And only has one solution <<<<Like that?

Answer 41

Well, there were two questions. WHat makes them the same, which is the -2 solution, and then what makes them different. FOr that one... let me see...


what makes the two equation so different is because the second equation is touching the x-axis when graphing, and the first equation is goes through the x - axis which gives it to x - intercepts.And only has one solution

becomes

What makes the two equation different is that the second equation is touching the x-axis in only one place when graphing but the first equation is goes through the x-axis which gives it two x - intercepts.

Same thing you said. Just moved one little bit.

Answer 42

Oh, and I missed "is goes" is going or just goes

Answer 43

Loll wow !Thanks

Answer 44

See how it makes it a bit more clear when you say touching makes one answer? That clarifies what you mean by "it touches."

Answer 45

Yeah it really does

Answer 46

It also helps when you see things from more that one source. Your book says one thing, but you may not get it all. Your brother may say another, but you don't get it all. I say a 3rd, an you don't get it all. However, you add together these little bits and you get more than you learned from any one place.

So for this topic, factoring, I suggest going over this set of three pages:
http://www.purplemath.com/modules/simpfact.htm

They show lots of examples and go over things step by step. They also have links to all the other terms they use, so if you never saw something or forgot it, you can look it up very easy. One of my two favorite references for Algebra.

Answer 47

The other site that has great examples is this one:
http://www.regentsprep.org/Regents/math/ALGEBRA/math-ALGEBRA.htm

I have seen many ways of explaining things there that are just so wonderful and understandable.... but navigating it can be a bit hard. So I use Google searches for the site to find things there.
https://www.google.com/search?q=site%3Aregentsprep.org+factor+grouping

That find me this page:
http://regentsprep.org/Regents/math/algtrig/ATV1/revFactorGrouping.htm

Which shows a powerful tool in quickly doing factor by grouping!

Answer 48

Thank you! stay awesome