How many parabollas can pass through 3 points $\displaystyle A(x_0,y_0),B(x_1,y_1),C(x_2,y_2)$
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only one
why?
Originally Posted by TheodorMunteanu How many parabollas can pass through 3 points $\displaystyle A(x_0,y_0),B(x_1,y_1),C(x_2,y_2)$ $\displaystyle y=ax^2+bx+c$ Solve: $\displaystyle \left\{\begin{matrix}y_0=ax_0^2+bx_0+c\\ y_1=ax_1^2+bx_1+c\\ y_2=ax_2^2+bx_2+c\end{matrix}\right$ And find $\displaystyle a,b,c$.
only one parabola if the axis of symmetry is parallel to the y-axis. (not really sure about this, yet) if the axis of symmetry can be any line in the xy plane ... how many ???
Originally Posted by TheodorMunteanu How many parabollas can pass through 3 points $\displaystyle A(x_0,y_0),B(x_1,y_1),C(x_2,y_2)$ What if $\displaystyle A,~B,~\&,~C$ are collinear?
Originally Posted by Plato What if $\displaystyle A,~B,~\&,~C$ are collinear? A line is a degenerate form of a parabola, so it's still only one parabola.
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