From elementary geometry we know that there is a unique straight line through any two points in a plane. Less well known is the fact that there is a unique parabola through any three noncollinear points in a plane. For each set of points below, find a parabola with an equation of the form y = ax2 + bx + c that passes through the given points. (Sketch the resulting parabola to check the validity of your answer.)
(a) (0, 1), (-1, 4), and (2, 1)
(b) (-3, 1), (-2, 2), and (-1, 5)
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