answer for math questions about parabolas

## y=x^2-2x+3?

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# 1 Answer

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

x^{2} -2x + 3 = 0

Factor it:

x^{2} -2x +3 = (x-3)(x+1) = 0

Thus the roots are x_{1} = 3 and x_{2} = -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.

## Comments

Wrong solution Grigori. Your factoring works for x

^{2}- 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:

x

_{1}= 1 + iv2, x_{2}= 1 - iv2because 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.

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