Finding the symmetry point in a quadratic graph

Question

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

If you're familiar with the quadratic formula, take the mean of the two roots of the quadratic equation and simplify the resulting expression.
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.
possible duplicate of Derivation of the formula for the vertex of a Parabola
Note that the graph of a quadratic equation has a line of symmetry, not a point of symmetry.

Peragon · Answer 1 · 2011-11-25 00:12:20Z

up vote 2 down vote

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

edited Nov 25 '11 at 0:12

answered Nov 24 '11 at 3:45

Peragon
413

3

Aren't you missing a minus sign in there? – J. M. Nov 24 '11 at 5:00

Good catch! Next time, just go ahead and fix it though :) – Peragon Nov 25 '11 at 0:13

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