Question

A quadratic function f(x) is hidden from view. You must find the maximum value of the function f(x). Choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently.

Answer 1

The form of the quadratic function that would be most efficient for finding the maximum value is vertex form:

f(x) = a(x - h)^2 + k

In this form, the vertex of the parabola is at the point (h, k), and the value of a determines the shape of the parabola. Specifically, if a is positive, the parabola opens upward, and the vertex is a minimum point. If a is negative, the parabola opens downward, and the vertex is a maximum point. Therefore, by looking at the value of a and the coordinates of the vertex, we can determine the maximum value of the function f(x).