Use the free Absolute Max & Min Calculator on ToolVexa to find the maximum and minimum of a quadratic function f(x) = ax^2 + bx + c over an interval.
How to Use
Enter a, b, c and the interval endpoints, then press Calculate.
Formula in Plain Words
A quadratic has a vertex at x = -b / (2a). Check the function at the two endpoints and at the vertex if it lies inside the interval, then pick the largest and smallest values.
Worked Example
For f(x) = x^2 - 4x + 3 on [0, 4], the maximum is 3.00 at x = 0.00 (also at x = 4.00) and the minimum is -1.00 at x = 2.00.
FAQs
What if the vertex is outside the interval?
Then the maximum and minimum are at the endpoints.
Does this work for a straight line?
No. This tool is for quadratics, so a must not be zero.
Can the maximum and minimum be equal?
Only if the function is constant on the interval, which a quadratic is not unless the interval is a single point.