Finding the equation of the parabola

[Chipset3600]

Hello guys, please help me, knowing that the parabola passes through the points A(0,1), B(-1,-2) e C(-2,7). How can i find the equation?

 

[MarkFL]

This question has also been posted on MHF for which responses have been given.

I don't want to see the folks here take the time to post help when it has already been given elsewhere. ;)

 

[soroban]

Hello, Chipset3600!

Find the equation of the parabola passing through: A(0,1), B(-1,-2), C(-2,7).

There are two such parabolas: one "vertical" [tex]\cup[/tex], the other "horizontal" [tex]\supset[/tex].Vertical: .[tex]y \:=\:ax^2 + bx + c[/tex]

Substitute the points and create a system of three equations.
The system has the solution: .[tex]a = 6,\:b = 9,\:c = 1[/tex]

The equation is: .[tex]y \;=\;6x^2 + 9x + 1[/tex]Horizontal: .[tex]x \;=\;ay^2 + by + c[/tex]

Substitute the points and create a system of three equations.
The system has the solution: .[tex]a = \text{-}\tfrac{2}{27},\:b = \tfrac{7}{27},\:c = \text{-}\tfrac{5}{27}[/tex]

The equation is: .[tex]x \;=\;\text{-}\tfrac{2}{27}y^2 + \tfrac{7}{27}y - \tfrac{5}{27}[/tex]

 

[MarkFL]

I didn't consider anything but the parabola with vertical axis of symmetry...I suppose we could find an infinite number of parabolas by rotating the axes by any angle we choose. (Cool)

 

[Chipset3600]

Thanks guys :)