Vertex and Axis of Symmetry Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Vertex and Axis of Symmetry.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept 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.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: The vertex is the extreme point of the parabola, and the axis of symmetry guarantees that for every point on one side, there is a matching point on the other.
Common stuck point: Remembering the formula x = -\frac{b}{2a} and correctly computing f at that value to get the y-coordinate of the vertex.
Sense of Study hint: Compute x = -b/(2a) first, then substitute that x-value back into the function to find the y-coordinate.
Worked Examples
Example 1
easySolution
- 1 Axis of symmetry: x = -\frac{b}{2a} = -\frac{8}{2} = -4.
- 2 Vertex y-value: f(-4) = 16 - 32 + 12 = -4.
- 3 Vertex: (-4, -4); axis of symmetry: x = -4.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.