Quadratic formula
SAT glossary · Math
Definition
x = frac-b ± √(b^2-4ac)2a, derived (not memorized) by completing the square on ax^2+bx+c=0. Read its structure: -b/2a is the axis and frac√(b^2-4ac)2a is the offset, so the roots sit symmetrically about the axis, displaced by an amount governed entirely by the discriminant.
Quadratic formula in plain English
The quadratic formula, x=frac-b±√(b^2-4ac)2a, gives you the solutions to any equation of the form ax^2+bx+c=0 — and rather than just memorizing it blindly, it's worth knowing it actually comes from 'completing the square' on that general equation. Breaking apart its structure reveals something useful: the piece -b/2a is exactly the parabola's axis of symmetry (its center line), while frac√(b^2-4ac)2a is how far the two solutions sit on either SIDE of that center. In other words, the two roots are always perfectly balanced around the axis, and how far apart they are is entirely controlled by the discriminant sitting inside the square root.
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