Vertex and Axis of Symmetry Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
If f(2)=7f(2) = 7 and the axis of symmetry is x=5x = 5, find f(8)f(8).

Solution

  1. 1
    The point (2,7)(2, 7) is 3 units left of the axis x=5x = 5.
  2. 2
    By symmetry, the mirror point is 3 units right: (8,7)(8, 7).
  3. 3
    So f(8)=7f(8) = 7.

Answer

f(8)=7f(8) = 7
Points equidistant from the axis of symmetry on opposite sides have the same yy-value. If x=5x = 5 is the axis, then f(5−d)=f(5+d)f(5-d) = f(5+d) for any dd.

About Vertex and Axis of Symmetry

The vertex of a parabola is the point where it reaches its maximum or minimum value. The axis of symmetry is the vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.

Learn more about Vertex and Axis of Symmetry →

More Vertex and Axis of Symmetry Examples

Example 1 easy

Find the vertex and axis of symmetry of [formula].

Example 3 easy

Find the axis of symmetry of [formula].

Example 4 medium

Is the vertex of [formula] a maximum or minimum?

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