Axis of symmetry
SAT glossary · Math
Definition
The vertical line x = -b/2a about which a parabola is symmetric; the vertex sits on it. A second route: if the roots r and s are known, the axis is their midpoint (r+s)/(2) — which doubles as a free check that computed roots are correct, since they must average to -b/(2a).
Axis of symmetry in plain English
A parabola (the U-shaped curve you get from graphing a quadratic like y=ax^2+bx+c) is perfectly symmetric — fold it right down the middle and the two halves match up exactly. That fold line is called the axis of symmetry, and its location is given by the formula x=-b/2a. The very tip of the parabola (its highest or lowest point, called the vertex) always sits exactly on this line. There's a second way to find it too: if you already know the parabola's two x-intercepts (call them r and s), the axis of symmetry is simply their midpoint, (r+s)/(2) — and this gives you a free way to double-check your work, since the roots you calculate should always average out to match -b/(2a).
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