Worksheet: Symmetry of Graphs

In this worksheet, we will practice identifying the axis of symmetry of a quadratic function given an equation, a vertex, or a graph.

Q1:

What is the axis of symmetry of the graph of the function 𝑓 ( 𝑥 ) = ( 𝑥 + 3 ) + 4 2 ?

  • A 𝑥 = 4
  • B 𝑥 = 3
  • C 𝑥 = 4
  • D 𝑥 = 3
  • E 𝑥 = 2

Q2:

Find the axis of symmetry of the quadratic equation 𝑦 = 2 𝑥 + 1 2 𝑥 1 2 .

  • A 𝑥 = 2
  • B 𝑥 = 6
  • C 𝑥 = 1 7
  • D 𝑥 = 3
  • E 𝑥 = 1

Q3:

Find the equation of the axis of symmetry of the function 𝑓 ( 𝑥 ) = 7 𝑥 1 4 𝑥 + 5 2 .

  • A 𝑥 = 1
  • B 𝑥 = 5
  • C 𝑥 = 7
  • D 𝑥 = 1
  • E 𝑦 = 2

Q4:

Find the equation of the axis of symmetry of the function 𝑓 ( 𝑥 ) = 𝑥 2 .

  • A 𝑥 = 1
  • B 𝑥 = 1
  • C 𝑥 = 2
  • D 𝑥 = 0

Q5:

Determine the equation of the line of symmetry of the curve.

  • A 𝑥 = 3
  • B 𝑥 = 5
  • C 𝑦 = 3
  • D 𝑦 = 5

Q6:

The point ( 1 8 , 2 ) is the vertex of a parabola described by a quadratic function. Find the equation of its axis of symmetry.

  • A 𝑥 = 2
  • B 𝑦 = 1 8
  • C 𝑦 = 1 8
  • D 𝑥 = 1 8

Q7:

What is the equation of the axis of symmetry of the graph of the function 𝑓 ( 𝑥 ) = 𝑥 1 6 𝑥 6 4 2 ?

  • A 𝑥 = 6 4
  • B 𝑥 = 1 6
  • C 𝑥 = 1 0
  • D 𝑥 = 8
  • E 𝑦 = 8

Q8:

Find the equation of the axis of symmetry of the function 𝑓 ( 𝑥 ) = 1 2 𝑥 1 3 + 2 𝑥 2 .

  • A 𝑥 = 3
  • B 𝑥 = 2
  • C 𝑥 = 6
  • D 𝑥 = 3
  • E 𝑦 = 6

Q9:

Find the equation of the axis of symmetry of the function 𝑓 ( 𝑥 ) = | 3 𝑥 | .

  • A 𝑦 = 3
  • B 𝑥 = 3
  • C 𝑦 = 3
  • D 𝑥 = 3

Q10:

In the graph below, find the axis of symmetry.

  • Athe origin
  • Bthe 𝑦 -axis
  • Cthe 𝑥 -axis

Q11:

The point ( 5 , 1 4 ) is the vertex of a parabola described by a quadratic function. Find the equation of its axis of symmetry.

  • A 𝑥 = 1 4
  • B 𝑦 = 5
  • C 𝑦 = 5
  • D 𝑥 = 5

Q12:

The point ( 1 2 , 5 ) is the vertex of a parabola described by a quadratic function. Find the equation of its axis of symmetry.

  • A 𝑥 = 5
  • B 𝑦 = 1 2
  • C 𝑦 = 1 2
  • D 𝑥 = 1 2

Q13:

Find the equation of the axis of symmetry of the function 𝑓 ( 𝑥 ) = | 6 𝑥 | .

  • A 𝑦 = 6
  • B 𝑥 = 6
  • C 𝑦 = 6
  • D 𝑥 = 6

Q14:

Determine the equation of the line of symmetry of the curve.

  • A 𝑥 = 1
  • B 𝑦 = 3
  • C 𝑦 = 1
  • D 𝑥 = 3

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