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anonymous
 one year ago
1. f(x) = 3  x2  6x
2. (x) = x2  8x + 2
I have these two problems. I need to find out the domain, range, maximum, and minimum for both of the above. I keep getting the wrong answers when I try it, and some that don't make sense.. Please help? Thanks in advance!
anonymous
 one year ago
1. f(x) = 3  x2  6x 2. (x) = x2  8x + 2 I have these two problems. I need to find out the domain, range, maximum, and minimum for both of the above. I keep getting the wrong answers when I try it, and some that don't make sense.. Please help? Thanks in advance!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can someone help me please!!?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1For a parabola with a positive leading coefficient, absolute maximum won't exit. (it opens up, and its absolute minimum is the vertex  ycoordinate is the value of the minimum, and xcoordintae is where this minimum is located)  For a parabola with a negative leading coefficient, absolute minimum won't exit. (it opens up, and its absolute maximum is the vertex  ycoordinate is the value of the maximum, and xcoordintae is where this maximum is located)  To find the vertex in each parabola, you need to complete the square. (for each function)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1``` If you are not familiar with what "perfect square trinomial" means, then I would advise to review that concept (here, with other people, or watch a video, read a book, get a tutor.... idk, that is your responsibility. I won't do it now, because I got to go pretty soon). ```

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1@macky342 You still there? Have you made any progress on the question, or still stuck? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm still stuck unfortunately.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1K, let's see if we can get somewhere...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0math has always been my worst subject. thank you.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Well, maybe we'll be able to turn that around. :) I'm taking a look...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great! Thank you. This is the last question i have in this class before i graduate so i just want to be done!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1First thing I'm going to do is rewrite the equations this way: \[f(x) = x^26x+3\] and \[g(x) = x^28x+2\].

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, now what do i do?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Alright, personally, for me a picture is worth a thousand words, so I'm going to set these up to make it easier to graph a picture.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1This is a trick that most classes don't teach you, but I'm going to factor an x out of the first two terms of each. The result looks like this:

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=x(x+6)+3\] and \[g(x)=x(x8)+2\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1You probably haven't seen that, but does that make sense so far?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, no worries, all I did is this for the first one \[ f(x) = x^26x+3 = x(x6)+3 = x(x+6)+3 \] So, I just ignored the 3, and factored an x out of the first two terms. Then, I took out the negative sign (I didn't have to but it looks nicer). Please let me know if you have any questions on this part. We may need to review factoring. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am not understanding a thing thats going on. i reviewed the chapter over 5 times. had a tutor try and explain it and my last hope was this website and i feel like theres still no hope :(

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Gotcha. No worries, there's just a mental block somewhere that we have to sort out. I've had plenty before myself. :) Let's start more basic.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1I'm going to do a few diagnostic questions (totally different than the current question) to see where your understanding starts. Does this make sense? \[x^2 + x = x(x + 1)\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, that's fine. Let's go simpler. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the x's is where i get lost.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm pretty good at basic math

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, so does this make more sense \[3^2 + 3 = 3(3+1)\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, so let's see if we can build on that understanding.... Let me think for a moment...

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.0Do you know that these two equations have graphs that are parabolas?

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.0In the first one, the x^2 term has a negative coefficient so it will look like this:

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.0In the second one, the x^2 term is positive so it will look like this:

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.0Does the first one have a high point or a low point?

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.0That high point is called a maximum point. It is also the vertex of the parabola.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1So, we know the first one has a maximum, but does it have a minimum too?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when i was trying what i knew it didn't. and i didn't know if that was right or not.. theres a space to enter it on my school work but i don't know what to put there if theres no minimum.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1You are right. There is no minimum for the first graph. You can just put 'no minimum' or if you want to be fancy you can say that the graph's minimum goes to 'negative infinity'

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0great! so what is the maximum? and i still need the range and the domain :(

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Good question. Let's see if we can track down the maximum first. Since you aren't comfortable with x's we are going to have to do this by "brute force" and plug in numbers until we see a pattern. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1No worries, though let's just try some obvious numbers. I'm assuming you are comfortable with plugging in numbers for x? Like f(x) = x^2  6x + 3 so if x = 0, then 0^2  6*0 + 3 = 3.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Basically, I just transform the x's into whatever number I like. Does that make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0kind of? I'm not too sure whats going on. I'm extremely tired right now. I'm a little older, i have a son who's a year and a half and he's sick so sleep and graduation are hard to balance on top of a child.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm trying here. let me look again.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Sure, I get the picture. Let me see if we can't get over the hump... How about this... You've heard the saying "X marks the spot" right?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1In math, it's the same idea, "x" marks the spot where some number should be.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1So, if I give you a formula, x + 10 you can replace the x (that marks the spot) with a number to see what I really mean.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1I could mean, 0 + 10, 1 + 10, 2 + 10, 3 + 10, or lots of other things. The point is, I can always turn a "x equation" into just simple math and numbers. I get to choose.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im understanding so far.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, so if we turn it up a notch, and I give you 5x + x now I have two x's that mark the spot. I can choose to replace these with a number, but it must be the same number. So, 5*1 + 1 or 5*2 + 2 but not, 5*1 + 50 or 5*3 + 100, I must pick the same number since the "x"s are the same.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Alright, so the formula we have has this symbol in it x^2. Do you know what this symbol means?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes the x has a exponent.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Good, and exponents tell us to multiply that number that many times. For example, 2^2 = 2*2 5^2 = 5*5 and so on

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, so let's see if we can figure out what on earth the original formula is saying. x^2  6x + 3 we have two "x"s (that mark the spot) so we get to pick a number to put in both spots.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, can we pick something easy like 2?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Sure, let's do that to start.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1So we have:  2^2 6*2 + 3 and we need to figure out what this means.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Alright, order of operations Please Excuse My Dear Aunt Sally, parentheses, exponents, multiplication/division addition/subtraction

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1So first, what is 2^2?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Good, so we have 4  6*2 + 3 next is multiplication

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Good! 4 12 + 3 this is easy now

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1"easier" that is... :) the negatives might be a little strange. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok will i miltiply 4 & 12 or what do i do since theres no symbol?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm decent when it comes to negatives.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1There's technically subtraction there.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Remember it was x^2 minus 6x plus 3 in the original formula x^2  6x + 3

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1So, we then get 4  12 + 3 = 16 + 3 = 13 I believe.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1This gets faster, don't worry. It takes a lot of words to describe the process. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is gonna take til 5am.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Hopefully not. :) So, believe it or not we have actually found a small piece of the parabola, we took x = 2 and got 13 as the result.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not even your fault, its mine..

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1This is graphed on the xyaxis like thisdw:1437103634210:dw

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, well we can keep plugging in numbers until the sun goes down (or comes up in your case), but I'm going to give you a small trick to use.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Always begin by using x = 0. After that use x = "the number in front of the x in the formula". Here's what I mean for the second part.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1We have x^2  6x + 3. We should use x = 0 and x = 6 because the 6 is sitting in front of the x without weird exponents.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1If we had x^2 + 10x + 3 we would pick x = 0 and x = 10. OK with that trick?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, so let's get started plug in x = 0 into the formula x^2  6x + 3 I will speed things up for you, you should get 0^2  6*0 + 3 = 0  0 + 3 = 3.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Actually scratch that, sorry. But I just found a better way that will take one step for you to use to find the maximum, we still need to plug in to use it though so our practice is not for nothing.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1The maximum or minimum of a parabola can be found by plugging in a special x. \[x = \frac{b}{2a}\] where b is the number sitting in front of the x without an exponent, and a is the number in front the x with an exponent. So, in x^2  6x + 3, a = 1 and b = 6. For x^2 + 10x + 40, a = 1 and b = 10. It's a bit of a magic trick why this works, but it works.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i fell asleep there for a minute too so that isn't helping

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1K, don't worry. I'm pulling out all the tricks I have here, Let me explain it one step at a time.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1We are looking at x^2  6x + 3 right? What number is in front of the x^2? Well, there is 1 there because there is a negative sign and 1 is always in front of any number.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1And what number is in front of the "x"? We already said that this was 6.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1The magic recipe says we want an x that is equal to b/2a. b is the number in front of the x a is the number in front of the x^2.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1So, we found that a = 1 (in front of x^2) and b = 6 (in front of x). The magic recipe is b/2a = (6)/2(1)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1This looks horrible, but if we just multiply the negatives in front we get (6)/2(1) = 6/2(1) and the 2 times 1 is 2 =6/2 then we get = 3. This is the magic x.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i kind of understand, lets just go with it.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1K, We now plug in x = 3 into the original formula x^2  6x + 3. This will give us the maximum that we were looking for (for the last 5 hours) (3)^2 6(3) + 3 = 9 +18 + 3 = 9 + 3 = 12.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry. its been such a struggle with me. i know it.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1No, no, I'm sorry it's taken me so long to figure out the best way to help you. It's totally fine. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i really appreciate it.. but now what?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, well we celebrate that we finally have the maximum is is 12. We know that the graph has no minimum, so the range gets as large as 12 and as small as negative infinity. We write this as \[Range \ is \ (\infty, 12]\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol how do i do the infinity symbol?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Is this an online assignment? maybe just type "infinity" in words I'm sure the teacher will be fine with that (hopefully). :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. he will fix it. he's nice.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what exactly is the domain?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Cool. For the domain, this has to do with what types of numbers can you plug in for x. There are problems with formulas like 10 divided by x, because 10 divided by 0 doesn't make sense. However, with our formula, we are find and can plug in whatever number we want. The domain is "all real numbers" or (infinity, +infinity)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the only problem is theres still one more equation lol

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Now, just for that last one... It's the same thing, just with different numbers. Let's slay this dragon once and for all. >:)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Alright, so now, x^2  8x + 2. What number in front of x^2? That's a = 1. What number in front of x? That's b = 8.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1What is the magic recipe? b/2a That gives us (8)/2(1) = 8/2 = 4. The magic x is 4. (Remember that this second graph has a minimum? This magic recipe will always find the maximum OR the minimum and it knows which one is which! Crazy, but true).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but doesn't the graph have no maximum?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1That's right. So this magic x will give us the minimum that we want. Pretty cool of it. The reason this works is because of Calculus, but let's not go there today... :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank god i don't need anymore math to graduate. lol

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1lol! Anyways, we now take x = 4, and replace this in our original formula x^2  8x + 2 4^2  8(4) + 2 = 16  32 + 2 = 16 + 2 = 14 if I'm not mistaken.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.014 is the minimum correct?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Yep! So, the minimum is 14. There is no maximum (or its +infinity). The range is [14, +infinity). The domain is fine so "all real numbers" or (infinity,+infinity).

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1I'm going to graph this on my graphing calculator just to confirm. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0great!! i really appreciate all of your help!!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1You are very welcome! I'm glad the dragon is dead now. lol :) Here's the second graph, and we are right.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1and the first one, is...... right again! Yay!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0great your amazing!! i appreciate it so much!! especially the patience you had!!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1No problem! I'm glad to help! Great effort on your end as well, you stuck it out and survived to tell the tale. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Go get some rest, your brain is probably deep fried. :)
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