Question

Write a quadratic function that has a minimum value and how do you know it has a minimum value?

Answer 1

Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f. If a < 0, then the parabola opens down, and it is a minimum functional value of f.