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Algebra 2 & Trigonometry Flashcards

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Questions and Answers

What is a Quadratic Equation?

An equation of the form ax² + bx + c = 0, where a ≠ 0 (correct)

An equation with a degree higher than 2

An equation of the form ax + b = 0

An equation of the form x² + y² = 1

What is the sum of the roots of a quadratic?

-b/a

What is the product of the roots of a quadratic?

c/a

The Quadratic Formula is _____

(-b ± √(b²-4ac)) / (2a) Signup and view all the answers

What value completes the square?

(b/2)² Signup and view all the answers

What is the Discriminant?

b²-4ac Signup and view all the answers

Describe the roots if b²-4ac=0.

real, rational, equal Signup and view all the answers

Describe the roots if b²-4ac>0.

real, rational or irrational, unequal Signup and view all the answers

Describe the roots if b²-4ac<0.

complex, conjugate pairs Signup and view all the answers

Study Notes

Quadratic Equations

A quadratic equation takes the standard form: ax² + bx + c = 0, with the condition that a ≠ 0.

Roots of Quadratics

The sum of the roots of a quadratic equation is given by the formula: -b/a.
The product of the roots is determined by the formula: c/a.

Quadratic Formula

The quadratic formula, used to find the roots of a quadratic equation, is not provided but generally is: x = (-b ± √(b² - 4ac)) / (2a).

Completing the Square

The value needed to complete the square in a quadratic equation is (b/2)².

Discriminant

The discriminant, denoted as b² - 4ac, is crucial for determining the nature of the roots.

Nature of Roots Based on the Discriminant

If b² - 4ac = 0, the equation has real, rational, and equal roots.
If b² - 4ac > 0, the equation has real, unequal roots that can be either rational or irrational.
If b² - 4ac < 0, the equation has complex, non-real roots.

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Description

This quiz consists of flashcards that cover essential concepts in Algebra 2 and Trigonometry, specifically focusing on quadratic equations. Each card presents key definitions and formulas, such as the quadratic formula and discriminant. Sharpen your understanding of these foundational mathematical topics through targeted review.