Is it likely to get a parabola to fit when there are four or more points it must pass through?

Question

Assuming that the x-values are distinct (what if they are not?)

Answer 1

fairly unlikely.

while curve fitting remember this. if you have n data points, you can exactly fit a curve of power n-1. For example, 2 data points can be fit with a line. power n-1= 1. ie y = ax + b right? three data points can be perfectly fit with a quadratic. etc..

a parabola can exactly fit three data points and maybe fit 4 or more data points depending on the data points.

if x values are not distinct, you have a parabola that opens to the right or left.


iron duke.....

y^2 = x is a function and it is a parabola. x is not distinct. same x gives different y's. opens to the right. it perfectly fits the points....

(0,0), (1,1), (1,-1), (4, 2), (4, -2), etc.

Answer 2

It is only a special case where you can fit a parabola to a set of 4 points, you can fit a parabola to any set of 3 points, and there are an infinite number of parabolas that can be fit to a set of 2 points.

Answer 3

Everyone is overlooking something in their answers. Namely, a parabola need not be a function. You can 'rotate' a parabola so that its symmetry line has any slope.

If you allow for such rotations then YES YOU CAN fit a parabola very easily to most groups of four points. You could search for these parabolic type of equations (parametrically defined) on the net to find out more.

Answer 4

Presicely to my information nopey dopey beary bopey


NOOOO!!!!!!!!!!!!!!!!
while curve fitting remember this. if you have n data points, you can exactly fit a curve of power n-1. For example, 2 data points can be fit with a line. power n-1= 1. ie y = ax + b right? three data points can be perfectly fit with a quadratic. etc..

a parabola can exactly fit three data points and maybe fit 4 or more data points depending on the data points.

if x values are not distinct, you have a parabola that opens to the right or left.


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y^2 = x is a function and it is a parabola. x is not distinct. same x gives different y's. opens to the right. it perfectly fits the points....

(0,0), (1,1), (1,-1), (4, 2), (4, -2), etc.

Answer 5

I don't think so. Like a circle, a parabola is a very typical kind of curve, and it isn't easy to just find a parabola to fit in for 4 points.

Answer 6

If we have three points, YES, a parabola will fit..

"likely".. NOPE.. there are more points that are NOT on the parabola than on the parabola....by using three points to find a parabola, we can always do ths.. then we have to ask, "is the fourth point on the parabola?" not too likely!

:)

Answer 7

It depends on your definition of a parabola. If it is a function f(x) = a*x^2 + b*x +c, the answer is no. Otherwise, for the general form of the function, the answer is yes.

Answer 8

No. a parabola y=ax^2 +bx+c can be made to pass through three pointsby suitably choosing a,b and c( 3 equations and 3 constants).

Answer 9

No, it is very unlikely.

If the x values are not distinct, then you do not have a function and hence do not have the graph of a continuos function.

Answer 10

a parabola has unlimited anount of points because graphs never stop