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The parabola of a quadratic function

Age 15 · Maths

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The graph of a quadratic function is a smooth curve called a parabola. It is mirror-symmetric, and it has one turning point that is either its lowest or its highest point.

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In the picture

  1. The parabola: the smooth curve drawn by a quadratic function
  2. The axis of symmetry: a vertical line that splits the curve into two mirror halves
  3. A point on the curve: its mirror twin on the other side sits at the same height
  4. The vertex, a minimum: the lowest point when a is positive
  5. The vertex, a maximum: the highest point when a is negative

Examples

  • A ball thrown in the air follows a downward parabola, peaking at its highest point.
  • The cable of a suspension bridge between two towers dips in a shape close to an upward parabola.

Key takeaways

  • If a is positive the parabola opens upward and has a minimum; if a is negative it opens downward and has a maximum.
  • Points at equal distance from the vertical axis of symmetry have the same height.

Quiz: The parabola of a quadratic function (Age 15)

  1. A quadratic function has a positive a. What does its parabola look like?

    • It opens upward and has a maximum
    • It opens upward and has a minimum
    • It opens downward and has a minimum

  2. Two points of a parabola lie on opposite sides of the axis of symmetry, at the same distance from it. How do their heights compare?

    • They are at the same height
    • Their heights are opposite numbers
    • The one on the right is higher

  3. What is the axis of symmetry of a parabola?

    • A vertical line that splits the curve into two mirror halves
    • A horizontal line that separates the curve into an upper and a lower part
    • A slanted line that touches the curve at the vertex

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Maths, Age 15