Vertex Form Calculator
Convert a quadratic equation from standard form to vertex form. Find the vertex, axis of symmetry, opening direction, discriminant, and roots with clear step-by-step working.
Enter quadratic coefficients
Result
Vertex form formula
For y = ax² + bx + c, the vertex coordinates are h = −b/(2a) and k = f(h).
Quick interpretation
a < 0: parabola opens downward
|a| > 1: narrower parabola
0 < |a| < 1: wider parabola
Frequently asked questions
What is vertex form?
Vertex form is y = a(x − h)² + k, where (h, k) is the vertex of the parabola.
How do you convert standard form to vertex form?
Use h = −b/(2a), calculate k = f(h), then substitute a, h, and k into y = a(x − h)² + k.
What happens when a equals zero?
The equation is no longer quadratic, so it cannot be written as a parabola in vertex form.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
