Algebraic Approach

It is known, from Pre-Calculus Algebra, that a quadratic equation of the form

f(x) = ax2 + bx + c, a > 0

has a minimum point with x-coordinate

h = -b/2a

and y-coordinate

k = f(h)

In this problem, x = t and f = W, and W(t) is a quadratic function with a = 0.03 > 0, b = -0.39, and c = 7.3. Thus, the day of the minimum weight occurs at

t = -(-0.39)/(2*0.03) = 6.5

with the minimum weight (in pounds) of

W(6.5) = 0.03(6.5)2 - 0.39(6.5) + 7.3 = 6.0325

This is, of course, what we got using the other approaches.