Quadratic Formula Flashcards

Questions and Answers

What does it mean to justify in mathematical terms?

A postulate or theorem which enables a conclusion to be drawn.

What is a quadratic equation?

An equation where the highest exponent of the variable is 2, usually written as ax^2 + bx + c = 0.

What is the standard form of a quadratic equation?

y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0.

What is an imaginary number?

A number that when squared gives a negative result, defined as √(-1), denoted as i. Signup and view all the answers

Define a complex number.

A complex number can be expressed as a + bi, where a and b are real numbers and i is the imaginary unit. Signup and view all the answers

What is a complex conjugate?

The number with equal real part and imaginary part equal in magnitude but opposite in sign. Signup and view all the answers

What does completing the square involve?

A technique used to solve quadratic equations and evaluate integrals. Signup and view all the answers

What is the discriminant in a quadratic equation?

The number D = b^2 - 4ac determined from the coefficients of ax^2 + bx + c = 0. Signup and view all the answers

What is a root of a number?

A number which when multiplied by itself a given number of times equals the original number. Signup and view all the answers

What does zero represent in a mathematical context?

A pair of numbers whose sum is zero, e.g., +1 and -1. Signup and view all the answers

Study Notes

Vocabulary and Definitions

Justify: Postulate or theorem allowing a conclusion to be drawn; used in mathematical proofs to support statements.
Quadratic Equation: An equation where the variable's highest exponent is 2; standard form is ax² + bx + c = 0, e.g., 2x² + 5x - 3 = 0.
Standard Form of a Quadratic Equation: An equation of degree 2 written as y = ax² + bx + c; 'a', 'b', and 'c' are constants, with 'a' not equal to 0.
Imaginary Number: A number yielding a negative result when squared; represented as √(-1) denoted by 'i' or 'j'.
Complex Number: Can be expressed as a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, satisfying i² = -1.
Complex Conjugate: The number with the same real part as a complex number but with an opposite imaginary part; e.g., the conjugate of 3 + 4i is 3 - 4i.
Completing the Square: A method to solve quadratic equations, graph functions, and evaluate integrals; useful when factoring is impractical or to find irrational and complex roots.
Discriminant: Calculated as D = b² - 4ac from the coefficients of ax² + bx + c = 0; indicates the number and type of roots of the quadratic equation.
Root: A number which, when multiplied by itself a specified number of times, equals a given number; the square root of 9 is 3 (3 x 3 = 9).
Zero: A value representing a null quantity; the concept often illustrated through pairs such as +1 and -1 that sum to zero, often used in arithmetic problems involving positive and negative integers.

Description

Test your knowledge of the quadratic formula with these flashcards. Each card presents key terms and definitions that are essential for understanding this critical mathematical concept. Perfect for students looking to reinforce their learning and prepare for exams.