Quadratic Functions Quiz

Grade 9 · Math · Quiz

Test your knowledge of parabolas, vertex form, factoring, and the quadratic formula.

Questions

  1. What is the standard form of a quadratic function?

    1. y = mx + b
    2. y = ax² + bx + c
    3. y = a(x - h)² + k
    4. y = ax³ + bx + c
    Show answer

    Answer: y = ax² + bx + c

    Standard form is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

  2. The vertex of the parabola y = x² - 4x + 3 is at:

    1. (2, -1)
    2. (2, 1)
    3. (-2, -1)
    4. (4, 3)
    Show answer

    Answer: (2, -1)

    The x-coordinate of the vertex is x = -b/2a = 4/2 = 2. Plugging back: y = 4 - 8 + 3 = -1. Vertex is (2, -1).

  3. If the coefficient 'a' in y = ax² + bx + c is negative, the parabola opens downward.

    Show answer

    Answer: True

    When a < 0, the parabola opens downward (like an upside-down U), giving a maximum vertex.

  4. What are the roots of x² - 5x + 6 = 0?

    1. x = 2 and x = 3
    2. x = -2 and x = -3
    3. x = 1 and x = 6
    4. x = -1 and x = 6
    Show answer

    Answer: x = 2 and x = 3

    Factor: (x - 2)(x - 3) = 0, so x = 2 and x = 3. Check: 2×3 = 6 and 2+3 = 5.

  5. Using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, solve x² + 2x - 8 = 0. What are the solutions?

    1. x = 2 and x = -4
    2. x = -2 and x = 4
    3. x = 4 and x = -2
    4. x = 2 and x = 4
    Show answer

    Answer: x = 2 and x = -4

    a=1, b=2, c=-8. Discriminant = 4+32 = 36. x = (-2 ± 6)/2, giving x = 2 or x = -4.

  6. The expression b² - 4ac is called the ___ and determines the number of real solutions.

    Show answer

    Answer: discriminant

    The discriminant (b²-4ac) tells you: positive = 2 real roots, zero = 1 repeated root, negative = no real roots.

  7. Which form of a quadratic equation makes it easiest to identify the vertex?

    1. Standard form
    2. Factored form
    3. Vertex form
    4. Slope-intercept form
    Show answer

    Answer: Vertex form

    Vertex form y = a(x - h)² + k directly shows the vertex at (h, k), making it the easiest form for this purpose.

  8. A quadratic equation with a discriminant of zero has exactly two distinct real roots.

    Show answer

    Answer: False

    A discriminant of zero means there is exactly ONE repeated real root (also called a double root), not two distinct roots.

Get a personalized course on Quadratic Functions built around your child.