College Algebra
posted by Kameesha on .
1.Use completing the square to describe the graph of the following function. Support your answer graphically.
f(x) = 2x^2 + 4x + 5
2. Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. R(x) = 5x/x+7
The vertical asymptote(s) is/are x =
The horizontal asymptote(s) is/are y =
The oblique asymptote(s) is/are y =

f(x) = 2x^2 + 4x + 5
= 2(x^2  2x) + 5
= 2(x^2  2x + 1) + 5  2(1)
= 2(x1)^2 + 7
this is a parabola with vertex at (1,7), opening downwards, with roots at 1 +/ sqrt(14)/2
5x/(x+7) = 5  35/(x+7)
has a vertical asymptote at x=7
and a horizontal asymptote at y=5
no oblique asymptote, since the degree of top and bottom are the same.