Questions and Answers
What is a Quadratic Equation?
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 _____
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What value completes the square?
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What is the Discriminant?
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Describe the roots if b²-4ac=0.
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Describe the roots if b²-4ac>0.
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Describe the roots if b²-4ac<0.
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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.
