1. ## Quick Parabolas

Three points define a "Quick" Parabola.

You can move the points around and press "Activate" to see the parabola

Two questions:

and (this one I want to know)

Can all parabolas be quick parabolas?

If you don't see the diagram then you can't do this.

Press the red "X" at the bottom right corner of the diagram to remove the parabola...

2. Three points define a "Quick" Parabola
Three non-colinear points. Because otherwise the determinant of the 3x3 linear system is zero.

And further, some parabolas have the form,
$\displaystyle Ax^2+By^2+Cxy+Dx+Fy+D=0$
In that case 3 points is not sufficient.
You need 6 (and I forgot the conditions on them).

But for a "standard" parabola,
$\displaystyle y=ax^2+bx+c,a\not = 0$
You have a unique parabola.

3. Originally Posted by ThePerfectHacker
Three non-colinear points. Because otherwise the determinant of the 3x3 linear system is zero.
Yes, I meant to say non-colinear...
But I did not use a matrix to make them.
And further, some parabolas have the form,
$\displaystyle Ax^2+By^2+Cxy+Dx+Fy+D=0$
In that case 3 points is not sufficient.
You need 6 (and I forgot the conditions on them).
Really? Cause it seems like it covers all the kinds of parabolas...

4. Originally Posted by Quick
Yes, I meant to say non-colinear...
But I did not use a matrix to make them.

Really? Cause it seems like it covers all the kinds of parabolas...
Select three non-colinear points. You can create one parabola through them that has a vertical axis of symmetry. You can create one parabola through them the has a horizontal axis of symmetry. You can create one parabola through them that has an axis of symmetry parallel to the line y = x. etc.

-Dan