Quadratic Functions Quiz

Grade 10 · Math · Quiz

Test your knowledge of parabolas, vertex form, and quadratic equations.

Questions

1. Which form of a quadratic equation most directly reveals the vertex?

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

   Answer: Vertex form

   Vertex form f(x)=a(x-h)²+k directly shows the vertex as (h,k).

2. What are the x-intercepts of f(x) = (x - 2)(x + 5)?

   1. x = 2 and x = -5
   2. x = -2 and x = 5
   3. x = 2 and x = 5
   4. x = -2 and x = -5
   Show answer

   Answer: x = 2 and x = -5

   Setting each factor to zero: x-2=0 gives x=2, x+5=0 gives x=-5.

3. A quadratic with discriminant = 0 has exactly one real root.

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   Answer: True

   Discriminant=0 means the parabola is tangent to the x-axis at exactly one point.

4. The axis of symmetry for f(x) = x² - 6x + 8 is:

   1. x = 3
   2. x = -3
   3. x = 6
   4. x = -6
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   Answer: x = 3

   x = -b/(2a) = -(-6)/(2·1) = 6/2 = 3.

5. The graph of a quadratic function is called a ___.

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   Answer: parabola

   All quadratic functions graph as parabolas — symmetric U-shaped curves.

6. For f(x) = -2x² + 4x - 1, the parabola:

   1. Opens upward with a minimum
   2. Opens downward with a maximum
   3. Opens upward with a maximum
   4. Opens downward with a minimum
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   Answer: Opens downward with a maximum

   Leading coefficient a=-2 < 0, so the parabola opens downward and has a maximum.

7. The vertex of f(x) = x² + 4x + 4 is at (-2, 0).

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   Answer: True

   x²+4x+4=(x+2)², so f(x)=(x+2)². The vertex is at x=-2, f(-2)=0, giving (-2,0).

8. What is the y-intercept of f(x) = 3x² - 2x + 7?

   1. 7
   2. -2
   3. 3
   4. 0
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   Answer: 7

   The y-intercept is f(0)=3(0)²-2(0)+7=7. In ax²+bx+c, c is always the y-intercept.

9. In f(x) = a(x - h)² + k, the variable h represents the x-coordinate of the ___.

   Show answer

   Answer: vertex

   In vertex form, h is the x-coordinate and k is the y-coordinate of the vertex.

10. Which quadratic has no real roots?

    1. x² - 5x + 6
    2. x² + 2x + 5
    3. x² - 4
    4. x² - 3x
    Show answer

    Answer: x² + 2x + 5

    Discriminant of x²+2x+5 is 4-20=-16 < 0, so no real roots. The others all have non-negative discriminants.

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