Quadratic Vertex Calculator
How It Works
This quadratic vertex calculator uses established formulas to provide accurate results.
The basic rule:
- Vertex x = -b/(2a)
- Vertex y = a(-b/2a)² + b(-b/2a) + c
- Axis of symmetry: x = -b/(2a)
- a > 0: opens up (minimum), a < 0: opens down (maximum)
Results are estimates. Consult a professional for critical decisions.
Want to Actually Learn Algebra?
Calculators give you answers — but if you want to understand the math, Allday Everyday Math teaches Algebra 1 fast with structured lessons, worked examples, and practice quizzes that build real confidence.
Explore Allday Everyday Math →Frequently Asked Questions
What is the vertex of a parabola?
The vertex is the highest or lowest point on a parabola. For y = ax² + bx + c, the vertex is at x = -b/(2a). It is the turning point where the parabola changes direction.
How do I know if the vertex is a minimum or maximum?
If a > 0 (positive leading coefficient), the parabola opens upward and the vertex is a minimum. If a < 0, it opens downward and the vertex is a maximum.
What is the axis of symmetry?
The axis of symmetry is a vertical line x = -b/(2a) that passes through the vertex. The parabola is a mirror image on either side of this line.