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How do I find the symmetry point for a graph based on a quadratic equation?

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marked as duplicate by Sally, Daniel W. Farlow, Joel Reyes Noche, Najib Idrissi, vociferous_rutabaga Mar 31 '15 at 8:35

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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If you're familiar with the quadratic formula, take the mean of the two roots of the quadratic equation and simplify the resulting expression. – J. M. May 4 '11 at 13:47
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If a quadratic function y = f(x) is meant, then J.M.'s suggestion is apt. A general quadratic equation will have at least one line of symmetry. Exactly one in the case of a parabola, even in general position, and exactly two in the case of a hyperbola. An ellipse will have two lines of symmetry as well, with only a circle, two parallel lines, and two intersecting lines (the degenerate cases) exhibiting one or more point symmetries. – hardmath May 4 '11 at 14:22
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Note that the graph of a quadratic equation has a line of symmetry, not a point of symmetry. – Isaac May 4 '11 at 21:41

For an equation of the form $y= ax^2 + bx + c $ the axis of symmetry lies on the x-value $ \frac{-b}{2a}\ $.

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