+118613
1) Rom is concerned that we answer questions (do homework) instead of teaching the question askers.
He invites discussion on this.
Thank you Rom :)
Please comment on Rom's original thread:
http://web2.0calc.com/questions/i-m-concerned-that-we-are-just-doing-people-s-homework-for-them-that-s-no-way-to-encourage-people-to-actually-learn-the-math
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2) Inverse Function Question.
This is a very simple question (high level) but it really made me think. Thanks Rom.
http://web2.0calc.com/questions/maths-question_27015#r2
+118613 My turn to try:
f(x)=x^2+9x+18
y=0^2+9*0+18
y=0+0+18
y=18
You confused me with a new question. LOL
YES If f(x)= x^2 +9x+18 then the y [really f(x) ] intercept is 18
SO (0,18) would be one point on the graph. :))
y=x^2+9x+18 is a polynomial function
This is because the y is out the front by itself and There are a list of terms with x^(some integer) aded or subtracted together after the equal sign.
That is a VERY lay explanation but it will do for the moment. :))
The number that is tacked on the end, the constant, will always be the y intercept!
Now the highest power of x gives the number of directions that the graph will take (sort of anyway). This is called the degree of the polynomial.
Lets look at thes polynomial functions.
y=3x+7
y=3x^1 +7
the y intercept is 7
the highest power(degree) is 1 so it only has one direction. Bingo...It has to be a line!
y=7x^2+12x+5
The y intercept is 5
the degree is 2 so it has 2 directions. Bingo... It has to be a parabola
y=-6x^3-5x^2+12x
The y intercept is 0 (there is no constant...well there is it is an invisable 0)
The degree is 3 so it has 3 directions so it is (probably) like a sideways S
I say probably because occassionally the directions are not clear and they look more like little kinks in the graph. But don't worry about that.
Yours is y=x^2+5x+6
Tell me about its basic shape please. :))
+118613 Well, you should have put it on a new post but I can certainly try to help you learn.
f(x)=x^2+5x+6
You only just posted so I am assuming that you can answer straight away and I will try to talk you through this question. That is the best way to learn. :)
First you really need to recognise the basic shape.
Do you know what this will be?
Can you tell me why?
Can you tell me anything else that you already know about this?
Like maybe the y intercept?
Do you know what this will be? ..a slope?
Can you tell me why? ..because I don't see a 'y' in the equation to intersect the points.
Can you tell me anything else you know about this? I have tried to factor it out and it resulted in 0, I'm assuming I'm taking the wrong steps.
Thank you very much.
+118613 Ok that is a vey good point.
There is no y in the equations.
Here f(x) has been used instead of y so technically the vertical axis should be labelled as f(x) instead of y.
Just to make it less confusing I will change the equation from
f(x)=x^2+5x+6
to
y= x^2+5x+6
Now can you tell me anything about this? Hint: it is not a line.
Can you tell me what the y intercept is now? That is where x=0.
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This may be a slow process but you may get a lot more out of it if we interact with each other like this.
I'm not sure, is it a parabola or a slope maybe? The y intercept should be approx around 6?
+118613 NOTE: I wrote all this BEFORE i saw your last answer.
Is it reasonable for me to assume you used a graphing program to make that graph?
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To make it a little quicker, you also need to be able to factor
x^2+5x+6
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I will do a similar one and you see if you can copy the method for your one.
x^2+6x+8
I need to find two numbers that multiply to give +8 and add to give +6
Since they multiply to give a positive they must both have the same sign.
Since they add to give a positive as well, they must both be positive numbers.
ok so what multiply to give 8
1*8
2*4
that is it.
2+4 =6 so that is the pair we need, 2 and 4
so
x^2+6x+8=(x+2)(x+4)
now it is definitely your turn to give some input :))
+118613 y= x^2+5x+6
The y intercept is NOT around 6.
It is where x=0
Put x=0 into the equation.
y=0^2+5*0+6
y=0+0+6
y=6
The y intercept is EXACTLY 6
Yes, I used 'Desmos' as recommended by Rom earlier this week in a previous post, but it didn't show me the steps so I am still stuck. I want to learn :( Thank you for taking the time.
Ok, if f(x)=y, and y=0, then this should be simpler than I have made it out to be, oops.
My turn to try:
f(x)=x^2+9x+18
y=0^2+9*0+18
y=0+0+18
y=18
So is this all I have to do? Where does the factoring come in to play like you showed me like so:
"I will do a similar one and you see if you can copy the method for your one.
x^2+6x+8
I need to find two numbers that multiply to give +8 and add to give +6
Since they multiply to give a positive they must both have the same sign.
Since they add to give a positive as well, they must both be positive numbers.
ok so what multiply to give 8
1*8
2*4
that is it.
2+4 =6 so that is the pair we need, 2 and 4
so
x^2+6x+8=(x+2)(x+4)"
+118613 My turn to try:
f(x)=x^2+9x+18
y=0^2+9*0+18
y=0+0+18
y=18
You confused me with a new question. LOL
YES If f(x)= x^2 +9x+18 then the y [really f(x) ] intercept is 18
SO (0,18) would be one point on the graph. :))
y=x^2+9x+18 is a polynomial function
This is because the y is out the front by itself and There are a list of terms with x^(some integer) aded or subtracted together after the equal sign.
That is a VERY lay explanation but it will do for the moment. :))
The number that is tacked on the end, the constant, will always be the y intercept!
Now the highest power of x gives the number of directions that the graph will take (sort of anyway). This is called the degree of the polynomial.
Lets look at thes polynomial functions.
y=3x+7
y=3x^1 +7
the y intercept is 7
the highest power(degree) is 1 so it only has one direction. Bingo...It has to be a line!
y=7x^2+12x+5
The y intercept is 5
the degree is 2 so it has 2 directions. Bingo... It has to be a parabola
y=-6x^3-5x^2+12x
The y intercept is 0 (there is no constant...well there is it is an invisable 0)
The degree is 3 so it has 3 directions so it is (probably) like a sideways S
I say probably because occassionally the directions are not clear and they look more like little kinks in the graph. But don't worry about that.
Yours is y=x^2+5x+6
Tell me about its basic shape please. :))
Thank you! That was an excellent explanation, it really helped.
To answer your question, let's see, the basic shape is a parabola because of the x^2 (wavering on a graph), in other words, it's not a simple line.
So I'll try to do these two exercises on my own, please correct me if they're wrong:
f(x)=x^2+5x+6
y=0^2+5*0+6
y=0+0+6
y=6 or (0,6)
f(x)=2x^2+10x+12
y=2*0^2+10*0+12
y=0+0+12
y=12 or (0,12)
+118613 I am gald I can help. Like Rom I get frustrated about answering questions when I know I am usually not teaching anything to anyone. I would much rather put the time in on someone that I think I am actually facilitating learning for :))
Now yes, both of thos times you found the y intercept of the graph. That is just one point but it is a start.
Now I want to go back to the questions examples that i used before.
The leading coefficient is the number in front of the highest power of x. Whether it is positive or negative is very important in deciding the shape of the polynomial graph.
If it is positive then the graph will begin in the top right corner, that is the first quadrant. Both x and y are positive here.
If the leading coefficient is negative the graph wil begin in the bottom right hand quadrant. Where x is positive but y is negative.
Use Desmos to help you see what I am saying. If you can't work it out then tell me.
https://www.desmos.com/calculator
y=3x+7
y=3x^1 +7
the y intercept is 7
the highest power(degree) is 1 so it only has one direction. Bingo...It has to be a line!
The leading coefficient is +3 so this will beginning in the top right. (It is a line with a positive slope!)
y=7x^2+12x+5
The y intercept is 5
the degree is 2 so it has 2 directions. Bingo... It has to be a parabola
The leading coefficient is +7. It starts in the top right. It is a concave up parabola!
y=-6x^3-5x^2+12x
The y intercept is 0 (there is no constant...well there is it is an invisable 0)
The degree is 3 so it has 3 directions so it is (probably) like a sideways S
I say probably because occassionally the directions are not clear and they look more like little kinks in the graph. But don't worry about that.
The leading coefficient is -6 So it will begin in the bottom right. It will look a bit like an upside down N
You should try some now:)
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I did this post ages ago. It is a good one and well worth understanding. Take a look and see if you can work out what I am telling people :)
http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed
Maybe I am getting a bit carried away since you only asked about a parabola, but this is conceptual learning that I am trying to give you and if you get it it will help you enormously.
In this post the letters, a,b,c,d, etc are just numbers :)
If you don't get it we can go back and just talk about lines and parabolas. :)
I'm wondering if you could help me with algebra this coming week. I am willing to pay you.
Please contact me: My email is jo7bello@yahoo.it
+118613 Firstly, are you the same guest that I have been woking with here?
I am more than happy to teach you on the forum for free, I am not here to get work for myself.
Good quality private tuition would probably help you enormously, it does for many people, but it is much better if it is face to face.
Anyway if you want to talk to me more you will need to become a member and approach me via private messaging. :))
