Power Calculators

V Quadratic Vertex Calculator

Find the vertex and axis of symmetry of a quadratic y = ax² + bx + c.

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Also available in our Android app, with charts and full breakdown tables.

📘 About the Vertex

Find the turning point of a quadratic function.

🧮 Formula

Where

  • a,b,c = quadratic coefficients
  • (xv,yv) = vertex
xv = -b/(2a); yv = a*xv² + b*xv + c.

✏️ Worked example

y = x² - 4x + 3

You enter
a1
b-4
c3
You get
Vertex x2
Vertex y-1

The vertex is (2, -1).

Try this example →

🧭 How to use this calculator

What you enter

  • a
  • b
  • c

What you get

  • Vertex x
  • Vertex y

💡 Shape

  • a > 0 means the parabola opens upward.
  • a < 0 means it opens downward.

❓ Frequently asked questions

What is the axis of symmetry?

It is the vertical line x = xv, where xv = -b/(2a).