📈

Quadratic Equations & Systems of Equations

116 cards · 🇺🇸 English

Solving quadratics (factoring, the quadratic formula) and systems of equations.

algebraquadratic-equationssystems-of-equations

Study all 116 cards for free

Flashcards, quizzes, pixel-art games and a daily review that remembers for you.

Study this deck free

Try the first 10 cards

1 / 10
Question

Quadratic equation

Knew itLearning

Tap the card for the answer · swipe right if you knew it, left if not

Already have an account? Sign in

Cards

  1. 1Quadratic equation
    An equation that can be written in the form ax² + bx + c = 0, where a ≠ 0
  2. 2Coefficients a, b, and c called in ax² + bx + c = 0
    a is the quadratic coefficient, b is the linear coefficient, c is the constant coefficient or free term
  3. 3Solutions of a quadratic equation
    Solutions, roots, or zeros of the quadratic function
  4. 4How many solutions does a quadratic equation have at most?
    At most two solutions
  5. 5Double root
    When there is only one solution, counted twice (also called a repeated root)
  6. 6What degree is a quadratic polynomial?
    Second degree, since the greatest power is two
  7. 7If a = 0 in ax² + bx + c = 0, what type of equation is it?
    Linear, not quadratic (assuming b ≠ 0)
  8. 8Can a quadratic equation have zero real solutions?
    Yes, when there are two complex conjugate solutions (discriminant is negative)
  9. 9Standard form of a quadratic equation
    ax² + bx + c = 0, where a, b, c are known numbers and a ≠ 0
  10. 10Quadratic formula
    x = (-b ± √(b² - 4ac)) / (2a)
  11. 11What does the ± symbol mean in the quadratic formula?
    It indicates there are two solutions: one using + and one using −
  12. 12Discriminant
    The expression b² - 4ac under the square root in the quadratic formula
  13. 13The discriminant is positive
    There are two distinct real roots
  14. 14The discriminant is zero
    There is exactly one real root (a double root)
  15. 15The discriminant is negative
    There are two distinct complex conjugate roots (no real roots)
  16. 16Symbol for the discriminant
    Usually an uppercase D or uppercase Greek delta (Δ)
  17. 17Factoring by inspection
    Expressing a quadratic equation as a product (px + q)(rx + s) = 0 by guessing factors
  18. 18Zero Factor Property
    If (px + q)(rx + s) = 0, then either px + q = 0 or rx + s = 0
  19. 19Factor x² + 5x + 6
    (x + 3)(x + 2)
  20. 20Vieta's rule for factoring
    For x² + bx + c = 0, find two numbers that add to b and multiply to c
  21. 21Completing the square
    A method that converts a quadratic equation into the form (x + p)² = q by adding a strategic term
  22. 22What algebraic identity is used in completing the square?
    (x + p)² = x² + 2px + p²
  23. 23What do you add to x² + bx to complete the square?
    (b/2)², the square of half the coefficient of x
  24. 24x² + 6x + 5 = 0 by completing the square (first step)
    x² + 6x = -5, then add (6/2)² = 9 to both sides: (x + 3)² = 4
  25. 25Reduced quadratic equation
    x² + px + q = 0, where the leading coefficient is 1 (divide original by a)
  26. 26Monic polynomial
    A polynomial whose leading coefficient is 1
  27. 27P in the reduced form x² + px + q = 0
    p = b/a from the original equation
  28. 28Quadratic formula for the reduced equation x² + px + q = 0
    x = (-p ± √(p² - 4q)) / 2
  29. 29Quadratic function
    A function of the form f(x) = ax² + bx + c
  30. 30What shape is the graph of a quadratic function?
    A parabola

And 86 more cards. Study the whole deck free

Articles about this deck

More Mathematics decks

See all
Study all 116 cards free