Practice Vertex and Axis of Symmetry in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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.

Fold the parabola along the axis of symmetry and both halves match perfectly. The vertex is at the fold—the very bottom of a U-shaped parabola or the very top of an upside-down one. It is the point where the function changes direction.

Example 1

easy
Find the vertex and axis of symmetry of f(x) = x^2 + 8x + 12.

Example 2

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

Example 3

easy
Find the axis of symmetry of y = 3x^2 - 12x + 5.

Example 4

medium
Is the vertex of y = -2(x-3)^2 + 10 a maximum or minimum?
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