Vertex

Definition

The vertex is the highest or lowest point on the graph of a quadratic function. It represents the maximum or minimum value of the function.

5 Must Know Facts For Your Next Test

1. The vertex form of a quadratic function is $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex.
2. For parabolas opening upwards, the vertex represents the minimum point; for those opening downwards, it represents the maximum point.
3. The $x$-coordinate of the vertex in standard form $ax^2 + bx + c$ can be found using $-\frac{b}{2a}$.
4. In an ellipse, vertices are points where the ellipse intersects its major axis.
5. The distance from any point on a parabola to its focus and directrix are equal at the vertex.

Review Questions

• What is the formula to find the $x$-coordinate of a vertex in a quadratic equation given in standard form?
• How does one convert a quadratic equation from standard form to vertex form?
• What role do vertices play in defining an ellipse?

Related terms

Axis of Symmetry:

A line that divides a figure into two symmetrical parts; for quadratics, it's given by $x = -\frac{b}{2a}$.

Focus:

A fixed point used with directrix to define conic sections like parabolas and ellipses.

Directrix:

A fixed line used with focus to define and construct conic sections.