Question

Is it possible to have a reciprocal of a quadratic function that has only one vertical asymptote? Is yes,

then give an example, if no, then explain why not

Answer 1

e.g.

y = (x-2)^2 = x^2 - 4x + 4 , which is a typical quadratic function

the reciprocal function:
y = 1/(x-2)^2
It has a vertical asymptote at x = 2

so in answer to your question ....
... if the original function has 2 different x-intercepts, then
its reciprocal function will have 2 different asymptotes
... If the original function is a perfect square, that is, it has only
one x=intercept, then its reciprocal will have 1 vertical asymptote

can you see how it would affect something like
y = x^2 + 4 ??