Question

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!

Answer 1

Can someone help me please!!?

Answer 2

For a parabola with a positive leading coefficient, absolute maximum
won't exit. (it opens up, and its absolute minimum is the vertex -
y-coordinate is the value of the minimum, and x-coordintae 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 -
y-coordinate is the value of the maximum, and x-coordintae is where
this maximum is located)
----------------------------------------------------

To find the vertex in each parabola, you need to complete the square.
(for each function)

Answer 3

```
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).
```

Answer 4

@macky342 You still there? Have you made any progress on the question, or still stuck? :)

Answer 5

I'm still stuck unfortunately.

Answer 6

K, let's see if we can get somewhere...

Answer 7

math has always been my worst subject. thank you.

Answer 8

Well, maybe we'll be able to turn that around. :) I'm taking a look...

Answer 9

Great! Thank you. This is the last question i have in this class before i graduate so i just want to be done!

Answer 10

First thing I'm going to do is rewrite the equations this way:
\[f(x) = -x^2-6x+3\] and \[g(x) = x^2-8x+2\].

Answer 11

okay, now what do i do?

Answer 12

Alright, 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.

Answer 13

This 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:

Answer 14

\[f(x)=-x(x+6)+3\] and \[g(x)=x(x-8)+2\]

Answer 15

You probably haven't seen that, but does that make sense so far?

Answer 16

not really :(

Answer 17

OK, no worries, all I did is this for the first one
\[ f(x) = -x^2-6x+3 = x(-x-6)+3 = -x(x+6)+3 \]
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. :)

Answer 18

i 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 :(

Answer 19

Gotcha. 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.

Answer 20

perfect. thanks.

Answer 21

I'm going to do a few diagnostic questions (totally different than the current question) to see where your understanding starts.

Does this make sense? \[x^2 + x = x(x + 1)\]

Answer 22

nope.

Answer 23

OK, that's fine. Let's go simpler. :)

Answer 24

the x's is where i get lost.

Answer 25

I'm pretty good at basic math

Answer 26

OK, so does this make more sense \[3^2 + 3 = 3(3+1)\]

Answer 27

yes

Answer 28

OK, so let's see if we can build on that understanding.... Let me think for a moment...

Answer 29

Do you know that these two equations have graphs that are parabolas?

Answer 30

yes.

Answer 31

In the first one, the x^2 term has a negative coefficient so it will look like this:

Answer 32

okay.

Answer 33

In the second one, the x^2 term is positive so it will look like this: