Maths Question ^_^ (1 Viewer)

[Pink Oni]

I've been studying lately and when proving for tests using graphs for values of x in Quadratic Trinomials, I just can't figure out how to tell whether I should graph a concave-up or concave-down parabola. I used to know how to do this but smarty-pants me had to not write it TT__TT

Can anybody suggest relations of this kind please?

 

[selablad]

I so don't understand the first part of the question...but I'll post anyway in case I manage to help someone out there...

If the coefficient of a (ax^2 + bx + c) is positive, it's a smiley parabola, if it's negative, it's a frowny parabola

I think. It's been a while since I did any maths...

 

[Pink Oni]

I so don't understand the first part of the question...but I'll post anyway in case I manage to help someone out there...

If the coefficient of a (ax^2 + bx + c) is positive, it's a smiley parabola, if it's negative, it's a frowny parabola

I think. It's been a while since I did any maths...

You're right, thanks for that. I kinda figured it out on my own while I was waiting for an answer lol, but at least I know now for sure

In any case, I have another question: When the Quadratic is Cubic, how do you graph it?

 

[lyounamu]

You're right, thanks for that. I kinda figured it out on my own while I was waiting for an answer lol, but at least I know now for sure

In any case, I have another question: When the Quadratic is Cubic, how do you graph it?

If the curve is cubic, see if you can factorise it. For example, (x-1)^3 = (x-1)(x^2 + x +1).

From here, you can see that the graph cross the x-axis at (1,0) and test either side to see if it is positive or not.

By the way, download winplot from internet. It will be of GREAT HELP to you. Trust me.

 

[Pink Oni]

If the curve is cubic, see if you can factorise it. For example, (x-1)^3 = (x-1)(x^2 + x +1).

From here, you can see that the graph cross the x-axis at (1,0) and test either side to see if it is positive or not.

By the way, download winplot from internet. It will be of GREAT HELP to you. Trust me.

Thank you so much, I will definitely do that

What if it is something like:
(x-y)(x+z)(x-a)

Or this one which I encountered lately during studies also:
(x-y)^2(x+z)(x-a)

(Where y, z and a are arbitrary values.)

 

[lyounamu]

Thank you so much, I will definitely do that

What if it is something like:
(x-y)(x+z)(x-a)

Or this one which I encountered lately during studies also:
(x-y)^2(x+z)(x-a)

(Where y, z and a are arbitrary values.)

That graph cross the x-axis at (y,0), (-z,0) and (a,0) and same for the other one. However, the shape of the graph will differ. Have a look at amused1977's post. His one is very concise and well-explained (better than mine ).

 

[Pink Oni]

Also, this is just harder 2U, not extension sorry. I haven't really gone in-depth with functions yet

 

[Pink Oni]

That graph cross the x-axis at (y,0), (-z,0) and (a,0) and same for the other one. However, the shape of the graph will differ. Have a look at amused1977's post. His one is very concise and well-explained (better than mine ).

I know that, I just don't know what the shape will be lol. I guess I'll just have to use winplot?

 

[Pink Oni]

Depends on the cubic.

If it's simply f(x) = x³ then it'll cross at (0,0) and plug in points.

If it's more complex like f(x) = x³ + 3x²+ 3x + 1 you'll need to:

1. Find the x intercept
2. Find the y intercept
3. Find stationary points, and find what "type" of points they are (maximum turning point/minimum turning point/inflexion point).

Findthing them:

Differentiate, and solve

SO in the above example, you see that
f'(x) = 3x²+ 6x + 3

Set y' = 0
0 = 3(x²+ 2x + 1)
0 = 3(x+1)²
x = -1
Plug into f(x)
y = 0

Station point @ (-1,o)

To find what type of points they are you can use the first derivative test or second derivative test. I ALWAYS use 2nd.

y"(x) < 0 ---> Maximum
y"(x) = 0 ---> Point of Inflexion
y"(x) > 0 ---> Minimum

When I say y"(x), I mean the second derivative, evaluated at each "x" (x values of each turning point)

4. Join the dots


Another useful program (apart from lyounamu's one) is graphmatica (freeware).

Thanks for this, but I'm not in-depth into functions yet sorry. Can you explain it in more simple terms for me please? Or do you recommend I look into functions early?

 

[lyounamu]

I know that, I just don't know what the shape will be lol. I guess I'll just have to use winplot?

It's hard to explain. Even if I do, you won't really get the visual aspect. Yeah, I do recommend you to use winplot. Download it now! (I am NOT advertising this).

 

[Pink Oni]

OK, thanks for that. And thanks to aMUSEd1977 as well, you've both been great help.

 

[Pink Oni]

Oh, tedious much? But if thats the simplest I can go I have no choice. Thank you. I'll have to get into functions before my exam if this happens then.

 

[st1m]

ok i don't understand your question much but this is what i can tell you:

if it is -x^2 than its negative which means it goes down, concave.

If its postive X^2 than its upwards.

 

[Pink Oni]

ok i don't understand your question much but this is what i can tell you:

if it is -x^2 than its negative which means it goes down, concave.

If its postive X^2 than its upwards.

Thanks, but that was already answered ~_^

 

[st1m]

lol ok... good luck in your exam, i had mine last term and it was 5 chapters including functions, just make sure you know your circle geometry and can tell what a semi-circle, hyperbola, porabola etc...

oh and our teacher likes to put proving questions, as in prove the formula of...

so good luck

 

[Sarah182]

Ok..

Step 1. Find the y intercept
Step 2. Find the x intercept

Create a table of values
x = -3, -2, -1, 0, 1, 2, 3

Find the y's, plot them and join the line

Exactly, its a pretty quick and easy system once you get into the routine.. or when there is 5 minutes left in the exam

 

[bored of sc]

Careful for the questions that have 2 x and/or y intercepts. E.g. y = x^2 - 4, be sure that you take positive and negative cases.

 

[Pink Oni]

lol ok... good luck in your exam, i had mine last term and it was 5 chapters including functions, just make sure you know your circle geometry and can tell what a semi-circle, hyperbola, porabola etc...

oh and our teacher likes to put proving questions, as in prove the formula of...

so good luck

Thanks for that info, I'll need it in two days Circle Geometry... Yuck xD

Careful for the questions that have 2 x and/or y intercepts. E.g. y = x^2 - 4, be sure that you take positive and negative cases.

Ah, never thought of that... Many thanks.

 

[Tsylana]

Heh...

I just think of it like this

Linear function ^1 - Generally starts and ends in Quadrants 3 & 1 respectively right?
Quadratic ^2- Starts 1 and 2 respectively
Cubic ^3- Starts 3 & 1 respectively
Quartic ^4- Starts 1 & 2 respectively

see a pattern...?

The odd powers start the same way a linear function will
And the even powers will start the same way a quadratic will

You can even take a hyperbola for an example

1/x = x is still to the power of 1 right? still follows the rule... roughly i guess =].


Now the only real exception is when u get a negative a terms in the functions... or if ur graph isnt big enough =P. So yeah =].

 

[x.Exhaust.x]

Ok..

Step 1. Find the y intercept
Step 2. Find the x intercept

Create a table of values
x = -3, -2, -1, 0, 1, 2, 3

Find the y's, plot them and join the line

Here's the graphmatica output (it's easier to just have an image)

http://i104.photobucket.com/albums/m170/mc_meaney/cubic.jpg

aMUSED aka Exphate is teh shizz in maths .