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answer for math questions about parabolas

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Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

Where are the qustions? Your parabola is opened up because the first coefficient is positive, The parabola has two roots defined by the equation

                                         x2 -2x + 3 = 0

Factor it:

                                     x2 -2x +3 = (x-3)(x+1) = 0

Thus the roots are   x1 = 3   and x2 = -1. The  axis of symmetry for the parabola is the midpoint of the segment [-1,3], which means x - coordinate of the vertex is  -1 + [3-(-1)]/2 =  1.  Because the parabola is opened up it has only minimum which is equal to y(1) = 2.


Wrong solution Grigori. Your factoring works for x2 - 2x - 3.

You are right. I messed up with the sign, being in hurry and didn't pay attention on it. The equation doesn't have a real solutions. Quadratic formula gives us:

                           x1 = 1 + iv2,  x2 = 1 - iv2

because the discriminanat is negative. There is no intersection with x -axis. The line of symmetry for the parabola is still the same: x = -b/2a, where b = -2 and a = 1. I apologize for accidental inaccuracy. Thank you for pointing to my miscalcultions.