How to find a quadratic function from a table of values?

[Tris Fray Potter]

HI! I'm not sure if this can go in precalculus or not because I'm from Australia, and our Maths subjects don't get that specific until university level.
1. Homework Statement
For my assignment on quadratic functions, I have to find the equation (the the form of ax^2+bx+c) for a table of values?

Homework Equations

I know how to use vertex form and change from vertex form to standard form and vice-versa
I have the co-ordinates:
(1,3)
(2,6)
(3,10)
(4,15)

The Attempt at a Solution

I think that I need to change it to vertex form, but I don't know how to do that, and I've spent the past couple of days trying to figure it out

Thanks in advance
Tris

 

[Jamison Lahman]

It has been a while since I've done anything like this, but the way I would go about solving this would be to plug the values of x into each equation to get the coefficients for each constant and then solving that as a system of equations. ex. (2,6) => a(2)^2+b(2)+c=6 => 4a+2b+c=6

 

[Simon Bridge]

I think you need a clear statement of what the problem is and what information you have. Unless you can be specific, you won't be able to solve the probelm. Pretend you are explaining the problem to someone who has not done Aussie maths courses - be as standard as possible.

For my assignment on quadratic functions, I have to find the equation (the the form of ax^2+bx+c) for a table of values?

You stuck a question mark on the end - do you not know?
Please type out the exact problem statement ... do you have a table of values given to you and you have to find which quadratic function best fits it? Or maybe you have to construct a table of values that people can look up to figure out which quadratic form they are dealing with ... ??

I see you have a bunch of coordinates - what are those coordinates of ?
ie. are they coordinates of points that are on the quadratic form?
Since you have a unary quadratic form and pairs of numbers ... you could just substitute the pairs into the general form and get the specific equation.

I think that I need to change it to vertex form, but I don't know how to do that,

... but earlier you said:

I know how to use vertex form and change from vertex form to standard form and vice-versa...

... which seems contradictory.
The result is we cannot know, with any confidence, what you are trying to describe.

Note: I'm in New Zealand.

 

[jedishrfu]

You could construct a set of linear equations in three unknowns a, b, and c by subbing in each point to get one of the equations and then use linear algebra to reduce it or use some prior method of subbing to reduce a out then b out to get c...

 

[Mark44]

I think you need a clear statement of what the problem is and what information you have. Unless you can be specific, you won't be able to solve the probelm.

The problem as stated seems pretty clear to me.

Homework Statement

For my assignment on quadratic functions, I have to find the equation (the the form of ax^2+bx+c) for a table of values?

The equation would be y = ax^2 + bx + c.

Homework Equations

I know how to use vertex form and change from vertex form to standard form and vice-versa
I have the co-ordinates:
(1,3)
(2,6)
(3,10)
(4,15)

The Attempt at a Solution

I think that I need to change it to vertex form, but I don't know how to do that, and I've spent the past couple of days trying to figure it out

No, you don't need to put the equation in vertex form. Just do as jedishrfu suggests, and substitute the four pairs of x- and y-values into the equation y = ax^2 + bx + c. I've checked, and can verify that all four of the given points lie on the same parabola.