Questions and Answers
What is the difference of squares?
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?
x = [-b ± sqrt(b^2 - 4ac)] / 2a
What is completing the square?
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What is the discriminant?
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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.
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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.
