Algebra
The quadratic formula
Derived by completing the square. The plus gives one root, the minus the other; their midpoint is always the vertex.
The Formula
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Derived by completing the square. The plus gives one root, the minus the other; their midpoint is always the vertex.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a | Leading coefficient | — | If zero, the equation is linear and this formula does not apply. |
| b | Linear coefficient | — | Sign matters absolutely — write b exactly as it appears in standard form. |
| c | Constant term | — | Everything must be moved to one side and collected before identifying a, b and c. |
What Each Symbol Means
a
Leading coefficient
If zero, the equation is linear and this formula does not apply.
b
Linear coefficient
Sign matters absolutely — write b exactly as it appears in standard form.
c
Constant term
Everything must be moved to one side and collected before identifying a, b and c.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to solve a quadratic equation page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Solve A Quadratic Equation, filed under Math. Every number the guide produces comes from substituting into this one line.