How you approach this depend upon whether or not you use a calculator.
1) The domain of the function is: -∞ < x < ∞
2) If you have to do this by hand, you may want to complete the square:
d(x) = 0.0125(x² - 80x + 1600) - 20
d(x) = 0.0125(x - 40)² - 20
This shows that the vertex occurs at (40, -20).
Substituting 0 for x gives you the point (0, 0).
Substituting 80 for x gives you the point (80, 0).
The parabola passes through these points.
3) The maximum depth of the dish occurs at the vertex; the depth will be 20 cm.
This is the minimum of the function, not the maximum.
4) Range: -20 ≤ y < ∞
5) Substituting 25 for x, d(x) = -17.1875.
Distance from vertex: 20 - 17.1875 = 2.8125; distance from top of dish: 17.1875 cm.
