Let's express L as a function of W: Now we plug L in terms of W into the formula for the area: Now we rearrange the terms of the last equation to get this: Now we complete the trinomial square on the right side of the equation.
But first we must factor out -1 from each of the terms on that side: Now we put the equation in what is called the vertex form for the equation of a parabola. This step is critical, because it tells us the maximum value for the function. This particular function has a maximum at the vertex, because the sign in front of the expression on the right side is negative, i. At that x value, which is W in our equation, the functional value is at a maximum.
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