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Quadratic Equations Flashcards

6 cards from real Algebra Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. What are the solutions to x² - 5x + 6 = 0?

    Answer: x = 2 and x = 3

    Factor as (x - 2)(x - 3) = 0, giving x = 2 and x = 3.

  2. What is the vertex form of a quadratic equation?

    Answer: y = a(x - h)² + k

    Vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

  3. What is the discriminant of 2x² - 4x + 2 = 0?

    Answer: 0

    Discriminant = b² - 4ac = (-4)² - 4(2)(2) = 16 - 16 = 0.

  4. A discriminant of zero means a quadratic has:

    Answer: One repeated real root

    A discriminant of zero means exactly one repeated real root where the parabola just touches the x-axis.

  5. Solve x² - 9 = 0 by factoring.

    Answer: x = ±3

    Factor as (x - 3)(x + 3) = 0, giving x = 3 or x = -3.

  6. What is the axis of symmetry for y = x² - 6x + 8?

    Answer: x = 3

    The axis of symmetry is x = -b/(2a) = -(-6)/(2·1) = 3.