Math guys - elementary school math question

[vote Republican]

Helping my 12 year old with some math, they are doing functions.

They get a table, values of X & Y, you have to find the function. I can find the function by trial and error, is there a better way to do this? I don't have the actual values in front of me, it's something like

X -3 -2 -1 ...... 6
Y 1 4 9 ......

I think it works out to 2x +5 or something similar, but just curious what's the best way to approach this type of problem?

[devildog2067]

If you're guaranteed that the function is a line, then you just calculate the slope and the intercept.

Choose any two points (x1, y1) (x2, y2). The slope is defined (in Euclidian Cartesian space) as (y2-y1)/(x2-x1). They're probably learning the slope-intercept form of a line, which is the standard place to start, so you'd then write y = mx + b. Then you plug in the slope you found for m, plug in either point's x,y for the x and y, and you're left with an equation with only 1 unknown. Solve for b and you're done.

It gets a bit harder if the function is not linear.

[fabricator]

Holy spit! They are doin that crap in elementary school?

[Annoyedgrunt]

Holy spit! They are doin that crap in elementary school?

Beat me to it! I have trouble with that function/graphing crap now, let alone when I was 12.

[PeterJasonMN]

Send him over to your mother's.

[fabricator]

Beat me to it! I have trouble with that function/graphing crap now, let alone when I was 12.

Function what now?:faint:

[BikerGoddess]

Um, did your kid bring home his textbook? The answer's likely somewhere in there. And he should be looking for it...

[OrangeJoe]

Um, did your kid bring home his textbook? The answer's likely somewhere in there. And he should be looking for it...

Biker Goddess, FTW.

[Daynja]

if you know the lowest point (or highest point if it's inverted) of the parabola you can use this equation:

y-k = a(x-h)²

where (h,k) is the lowest point. a is how wide or narrow it is. In your example it is 1. I assumed the vertex was (-4,0) so I get y=(x+4)² which is also y=x²+8x+16

Maybe there is a better way, but it's hard when the question presented is incomplete.

[PeterJasonMN]

Um, did your kid bring home his textbook? The answer's likely somewhere in there. And he should be looking for it...


Homeschooled.

[vote Republican]

If you're guaranteed that the function is a line, then you just calculate the slope and the intercept.

Choose any two points (x1, y1) (x2, y2). The slope is defined (in Euclidian Cartesian space) as (y2-y1)/(x2-x1). They're probably learning the slope-intercept form of a line, which is the standard place to start, so you'd then write y = mx + b. Then you plug in the slope you found for m, plug in either point's x,y for the x and y, and you're left with an equation with only 1 unknown. Solve for b and you're done.

It gets a bit harder if the function is not linear.

Not there yet. Just finding the function from a set of values. Range, domain, definition of a funciton, stuff like that.

[vote Republican]

Um, did your kid bring home his textbook? The answer's likely somewhere in there. And he should be looking for it...

We are using a textbook. This problem is out of the textbook, in fact. I'm just trying to see if there's a better method to solving this problem.

[vote Republican]

if you know the lowest point (or highest point if it's inverted) of the parabola you can use this equation:

y-k = a(x-h)²

where (h,k) is the lowest point. a is how wide or narrow it is. In your example it is 1. I assumed the vertex was (-4,0) so I get y=(x+4)² which is also y=x²+8x+16

Maybe there is a better way, but it's hard when the question presented is incomplete.

No, way too complicated. Imagine you have a formula y = 2x + 3

x y
-3 -3
-2 -1
-1 1
0 3
1 5
2 7
3 9

right?

All this problem is, is giving you the x & y values, and asking what is the equation that produces these values. I know you can figure it out by trial and error, I'm just asking is there a formal way to find the equation?

Anyone who can help, please post it up. Any social commentary, please keep it to yourselves.

[Daynja]

No, way too complicated. Imagine you have a formula y = 2x + 3

x y
-3 -3
-2 -1
-1 1
0 3
1 5
2 7
3 9

right?

All this problem is, is giving you the x & y values, and asking what is the equation that produces these values. I know you can figure it out by trial and error, I'm just asking is there a formal way to find the equation?

Anyone who can help, please post it up. Any social commentary, please keep it to yourselves.

Like the first guy said, it's easy if it's a straight line, but the first set of coordinates you gave was not from a straight line. This second set makes much more sense.

There are 2 easy ways to find the equation from coordinates like this. The first way requires the coordinates of 2 points, the other requires the slope and y axis intercept.

We can take any 2 points, lets use (-1,1) and (0,3). First, find the slope. this is (y1-y2)/(x1-x2) so: (1-3)/(-1-0) = 2. Now since you know the slope is 2 and you are given the y intercept (3) you can use slope intercept form like this: y=mx+b (m is slope, b is y intercept) this would be y=2x+3

or, you can go to point slope form:
y-y1=m(x-x1)

Lets use the point (0,3). y-3=2(x-0)

This is simplified as the same y=2x+3.

[vote Republican]

Got it. Thanks!

[Douglas in CT]

My brain hurts. ;)

[DBradD]

Like others typed, it's you just use the definition of a line if it's linear. Otherwise, there are special functions such as parabolas, ellipses, etc. that have standard equations. Beyond these, you get into curve-fitting and regression which obviously isn't what a 12 year old is trying to do.

The bottom line is that you plot the points and see if it's a line. If it is, then do what the ohter guys said. I have to think it is unless you've already covered parabolas, ellipses, circles, hyperbolas, etc. I think that stuff will be later.