Answer
The student worked around 29 hours each week.
Work Step by Step
Since g is given the equation will result as:
$2.97=-0.0006h^2+0.015h+3.04$
Subtracting both sides by 2.97 will result as:
$0=-0.0006h^2+0.015+0.07$
Using the quadratic formula, the number of hours (h) can be found:
$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
a=-0.0006, b=0.015, and c=0.07, so:
$h=\frac{-0.015\pm\sqrt{0.015^2-4(-0.0006)(0.07)}}{2(-0.0006)}$
$h=\frac{-0.015\pm\sqrt{0.000225+0.000168}}{-0.0012}$
$h=\frac{-0.015\pm\sqrt{0.000393}}{-0.0012}$
$h\approx\frac{-0.015\pm0.019824}{-0.0012}$
Since the positive option will result in a negative answer, the negative option will be used:
$h\approx\frac{-0.015-0.019824}{-0.0012}$
$h\approx\frac{-0.034824}{-0.0012}$
$h\approx29$
