Satellite dish antennas have the shape of a parabola. Consider a satellite dish that is 80 cm across. Its cross-sectional shape can be described by the function d(x) = 0.0125x^2 - x, where d is the depth, in centimetres, of the dish at a horizontal distance of x centimetres from one edge of the dish.

Question

Satellite dish antennas have the shape of a parabola. Consider a satellite dish that is 80 cm across. Its cross-sectional shape can be described by the function d(x) = 0.0125x^2 - x, where d is the depth, in centimetres, of the dish at a horizontal distance of x centimetres from one edge of the dish.
1. What is the maximum depth of the dish in cm?

Steve · Answer

0.0125x^2 - x = 1/80 x^2 - x = 1/80 (x^2 - x + 1/4) - 1/80 * 1/4 = 1/80 (x - 1/2)^2 - 1/320 max depth is 1/320 cm