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?
1. What is the maximum depth of the dish in cm?
Answers
Steve
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
= 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