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#### Chipset3600

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- Feb 14, 2012

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- Feb 14, 2012

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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]

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- Feb 14, 2012

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Thanks guys