Math 9 - Quadratic Equations

Flashcards covering key vocabulary and concepts related to quadratic equations, the nature of roots, and real numbers.

Discriminant

A value derived from a quadratic equation (ax² + bx + c = 0) that helps determine the nature of the roots (solutions).

Quadratic Equation

A polynomial of degree two, generally in the form ax² + bx + c = 0, where a ≠ 0.

Quadratic Term

The term 'ax²' in a quadratic equation.

Linear Term

The term 'bx' in a quadratic equation.

Constant Term

The term 'c' in a quadratic equation.

Quadratic Formula

A formula used to find the roots of any quadratic equation: x = (-b ± √(b²-4ac)) / (2a).

Extracting Square Roots

A method to solve quadratic equations when the equation has only quadratic and constant terms.

Quotient Rule

Applied when the equation has quadratic and linear terms only.

Factoring

Breaking down the quadratic into binomial factors to find roots.

Completing the Square

Transforming the equation into a perfect square trinomial to solve.

Zero Product Property

Setting each factor to zero and solving to find roots.

Discriminant

b² - 4ac, used to determine the nature of roots (real, equal, or imaginary).

Real Numbers

Includes all Rational and Irrational numbers.

Rational Numbers

Numbers that can be expressed as a ratio of two integers (fractions can be expressed as terminating or repeating decimals).

Irrational Numbers

All real numbers that are NOT rational; cannot be expressed as fractions, non-repeating, non-terminating decimals.

Integers

Positive and negative non-fraction numbers, including zero.

Whole Numbers

Positive Integers, including zero.

Natural Numbers

Counting Numbers (1, 2, 3, …).

The discriminant of the quadratic equation

b²-4ac. The value of the expression.

Sum of Roots

r₁ + r₂ = -b/a

Product of Roots

r₁ · r₂ = c/a