Question

A quadratic function f(x) is hidden from view. You must find the minimum 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.

1) Standard form: f(x) = ax�� + bx + c
2) Vertex form: f(x) = a(x - h)�� + k
3) Factored form: f(x) = a(x - r)(x - s)
4) None of the above

Answer 1

The most efficient form to find the minimum value of a quadratic function is the vertex form: f(x) = a(x - h)² + k. In this form, the vertex of the parabola (which represents the minimum or maximum value) is directly given by the values of h and k. To find the minimum value, you just need to find the y-coordinate of the vertex, which is k. No additional calculations or transformations are necessary.

Step-by-step explanation:

The most efficient form to find the minimum value of a quadratic function is the vertex form: f(x) = a(x - h)² + k.

In this form, the vertex of the parabola (which represents the minimum or maximum value) is directly given by the values of h and k.

To find the minimum value, you just need to find the y-coordinate of the vertex, which is k. No additional calculations or transformations are necessary.