Compare calculators

Both calculators run independently — change the inputs on either side to compare results.

Critical Points Calculator

Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.

x² Coefficient (a)

x Coefficient (b)

Fill in the required fields to see your result.

Calculus

Area Under Curve Calculator

Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂]. Use it to evaluate definite integrals for quadratic functions in physics, economics, or calculus coursework.

Coefficient of x²

Coefficient of x

Constant Term

Starting x-value

Ending x-value

Fill in the required fields to see your result.

Key differences

	Critical Points Calculator	Area Under Curve Calculator
Category	Calculus	Calculus
Inputs required	2	5
Result	Critical Point x-value	Area Under Curve (square units)
What it does	Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.	Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂]. Use it to evaluate definite integrals for quadratic functions in physics, economics, or calculus coursework.