Quadratic Equations and Square Roots Review

Vocabulary flashcards covering perfect squares, square roots, quadratic equations, and related solving techniques.

Perfect square

A number that can be written as the product of an integer and itself (e.g., 9 = 3 × 3).

Square root

A value that, when multiplied by itself, equals a given number (e.g., √9 = 3).

Simplified radical form

A square-root expression written after extracting all perfect-square factors (e.g., √45 = 3√5).

Quadratic equation

A second-degree polynomial equation that can be written in the form ax² + bx + c = 0 with a ≠ 0.

Standard form of a quadratic

The arrangement ax² + bx + c = 0, listing terms in descending powers and equated to zero.

Second-degree polynomial

Any polynomial whose highest exponent is 2; another name for a quadratic expression.

Coefficient "a"

The non-zero constant that multiplies x² in the standard form of a quadratic equation.

Coefficient "b"

The constant that multiplies x in the quadratic’s standard form ax² + bx + c = 0.

Constant term "c"

The term in ax² + bx + c = 0 that contains no variable; it is added or subtracted from the expression.

Square Root Property

If x² = c, then x = ±√c, providing both the positive and negative solutions.

± (plus-minus) symbol

Notation indicating both the positive and negative values of a quantity, commonly used after applying square roots.

Imaginary unit "i"

The symbol representing √−1; used when a square root involves a negative radicand, e.g., √−4 = 2i.

Square root method

A technique for solving quadratic equations by isolating the squared term and then applying the square root property.

Perfect vs. non-perfect square

Perfect squares yield integer roots (e.g., 9 → 3), whereas non-perfect squares produce irrational or radical roots (e.g., 45 → 3√5).