Consider 3 points with coordinates (0; 1), (1; 0) and (2; 3). Find a parabola passing through these points.
First, substitute the coordinates in the parabola equation y = ax2+bx+c and solve the set of equations 1=c, 0=a+b+c, 3=4a+2b+c. The solution is a = 2, b = -3, c = 1. Thus y = 2x2 - 3x + 1. The parabola vertex is (-b/2a; f(-b/2a)) = (-3/4; -1/8). a = 2 then the branches of the parabola are up-directed.
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