Consider f(x)=3ax−x2. write down a formula in terms of a for the maximum of f(x).

Using the vertex of the quadratic equation, it is found that the formula in terms of a for the maximum of f(x) is of:

A quadratic equation is modeled by:

The vertex is given by:

In which:

Considering the coefficient a, we have that:

In this problem, the function is:

The coefficients are a = -1, b = 3a, c = 0, hence:

More can be learned about the vertex of a quadratic equation at link

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