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Questions and Answers
What is the difference of squares?
What is the difference of squares?
What is a quadratic equation?
What is a quadratic equation?
An equation of degree 2 with the standard form y = ax^2 + bx + c where a cannot be 0.
What is the quadratic formula?
What is the quadratic formula?
x = [-b ± sqrt(b^2 - 4ac)] / 2a
What is completing the square?
What is completing the square?
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What is the discriminant?
What is the discriminant?
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What are zeros or roots?
What are zeros or roots?
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Study Notes
Difference of Squares
- Represents the expression x² - a², which is a subtraction of two squared numbers.
- Factors into (x + a)(x - a).
Quadratic Equation
- Defines a polynomial equation of degree 2 with the standard form y = ax² + bx + c.
- Coefficients a, b, and c are constants; a must not equal 0.
Quadratic Formula
- Utilized for solving quadratic equations, expressed as x = [-b ± √(b² - 4ac)] / (2a).
- Contains two potential solutions for the variable x, where a, b, and c represent constants.
Completing the Square
- A method of solving and graphing quadratic equations by manipulating the x-term's coefficient.
- Involves taking half of the x-term coefficient, squaring it, and adding to both sides; useful when factoring fails or for identifying irrational and complex roots.
Discriminant
- The expression b² - 4ac, found under the square root in the quadratic formula.
- Indicates the nature of the roots: two real solutions, one real solution, or two complex solutions based on the values of a, b, and c.
Zeros or Roots
- Represents solutions of a polynomial equation, i.e., values that make the polynomial equal to zero.
- Graphically corresponds to the points where the function intersects or touches the x-axis for real solutions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on quadratic equations with these flashcards. Each card introduces key terms and definitions that are essential to understanding quadratics. Perfect for reviewing important concepts in Algebra 1.
