Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
What is the difference of squares?
What is the difference of squares?
- A quadratic equation
- A squared number added to another squared number
- A squared number subtracted from another squared number (correct)
- The sum of two squared numbers
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?
Signup and view all the answers
What is the discriminant?
What is the discriminant?
Signup and view all the answers
What are zeros or roots?
What are zeros or roots?
Signup and view all the answers
Flashcards are hidden until you start studying
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.
