#### Answer

37.7 pounds

#### Work Step by Step

The amount of vitamins is modeled by:
$y=.149x^2-4.475x+406.478$
We are asked to find the weight of a child who should be receiving 600 micrograms. The equation then becomes:
$y=.149x^2-4.475x+406.478-600$
Once we simplify using subtraction, we use the quadratic formula.
$$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
Where b is the coefficient of the term with a variable raised to the first power, a is the coefficient of the squared term, and c is the coefficient of the term without a variable in front of it.
This gives the answer:
37.7 pounds