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Finding the equation of the parabola

Chipset3600

Member
Feb 14, 2012
79
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

Administrator
Staff member
Feb 24, 2012
13,775
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

Well-known member
Feb 2, 2012
409
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

Administrator
Staff member
Feb 24, 2012
13,775
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

Member
Feb 14, 2012
79
Thanks guys :)