Optimization

The optimization of a quadratic equation is the process to find the maximum or minimum of said quadratic.

Process

It involves converting a quadratic to the standard form by completing the square. Then by the Trivial Inequality, the maximum or minimum (it depends on which way the graph of the quadratic is facing) is .

"Formula"

To optimize a quadratic, one might use the method described above, or one could use this other, smoother, method:

If , then the quadratic reaches its minimum when , while when , the quadratic reaches its maximum when .