Question

A family of functions is given by
r(x) = 1/[a-(x-b)^2]
Assume a > 0, b > 0.

Find the vertical asymptotes of
r(x)

Answer 1

set the denominator equal to zero and solve for \(x\)

Answer 2

clear or no?

Answer 3

that make sense!

Answer 4

Vertical asymptotes will appear when division by 0 occurs, so that is why you want to find where the denominator is 0.

Answer 5

I can't seem to solve for the denominator to equal 0..

Answer 6

\[
a-(b-x)^2 = a - (b^2-2bx+x^2) = (-1)x^2 +(2b)x+(a-b^2)
\]

Answer 7

it looks like i can somehow use the quadratic formula right..? the answer I am supposed to get is both positive and negative

Answer 8

Yes, the solution must be in terms of a and b.