Question

1. The shape of a satellite dish is often parabolic because of the reflective qualities of parabolas. Suppose a particular satellite dish is modeled by the following equation.

0.5x^2 = 2 + y

a. Approximate the solution by graphing.
b. On the graph from part a, translate the parabola so that there is a double root.
Label this curve A.
c. Translate the parabola so that there are no roots. Label this curve B.

Answer 1

a. (Image)

b.
`(x^(2))/(2) - y = 2\\` has 2 real roots, i.e. 2 and -2

c.
`(x^(2))/(2) - y = n\\` where n is any negative real number