Power Calculators

min/max Quadratic Minimum Maximum Calculator

Find the minimum or maximum value of a quadratic y = ax² + bx + c.

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Fill in the details and click Calculate to see your results.


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

📘 About the Min / Max

Find the extremum of a quadratic over all real x.

🧮 Formula

Where

  • a > 0 = minimum
  • a < 0 = maximum
  • xv = location of extremum
xv = -b/(2a); yv = f(xv).

✏️ Worked example

x² - 6x + 5

You enter
a1
b-6
c5
You get
Minimum / Maximum value-4
At x3

The minimum value is -4 at x = 3.

Try this example →

🧭 How to use this calculator

What you enter

  • a
  • b
  • c

What you get

  • Minimum / Maximum value
  • At x

💡 Interpretation

  • If a is positive, the parabola opens upward and the vertex is a minimum.
  • If a is negative, the parabola opens downward and the vertex is a maximum.

❓ Frequently asked questions

What if a is zero?

Then the function is linear rather than quadratic, so this calculator does not apply.