Quadratic equation

An equation whose highest-degree term has degree two. In one variable, it can be written as ax² + bx + c = 0, with a ≠ 0.

Quadratic formula: A formula that gives the roots of ax² + bx + c = 0 from its coefficients. It solves every quadratic equation, including those that do not factor neatly.
Polynomial: An expression formed from variables and coefficients using nonnegative integer powers and arithmetic operations. A quadratic equation sets a degree-two polynomial equal to zero.
Projectile motion: The motion of an object launched into the air and acted on primarily by gravity. Under constant gravity, height varies quadratically with time, making impact time a quadratic solution.
Linear equation: An equation whose variables have degree at most one. Its graph is a line and it has at most one solution, unlike a quadratic.
Fundamental theorem of algebra: The theorem that every nonconstant polynomial with complex coefficients has a complex root. It guarantees that every quadratic has two complex roots when multiplicity is counted.
Completing the square: An algebraic method that rewrites a quadratic expression as a squared binomial plus a constant. It derives the quadratic formula and turns equations into a directly solvable square.
Coefficient: A numerical or symbolic factor multiplying a variable or another expression. The values a, b, and c determine a quadratic’s roots and graph.
Area optimization: The use of mathematical methods to find the largest or smallest possible area under constraints. Many fixed-perimeter problems produce a quadratic area function whose vertex gives the optimum.
Cubic equation: An equation whose highest-degree term has degree three. Its higher degree permits up to three roots and more varied graph shapes.
Complex plane: A coordinate plane in which the horizontal axis represents real parts and the vertical axis imaginary parts. Nonreal quadratic roots appear as points reflected across the real axis.

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