# Finding the symmetry point in a quadratic graph

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

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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
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
possible duplicate of Derivation of the formula for the vertex of a Parabola –  Isaac May 4 '11 at 21:40
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}\$.