[Limits] How to get the vertical asymptote

[bbl]

I'm familiar with getting the vertical asymptotes of rational functions. However, when it comes to radicals, I got stumped. How will I get the vertical asymptote of the problem below?

 

[pka]

What is a zero of $4x^2+3x+2~?$

 

[lookagain]

bbl, were you told that it has a vertical asymptote? Not all of those have vertical asymptotes. If the radicand
has no zeroes, then it has no vertical asymptotes. By the way, plotting it on WolframAlpha could be
misleading.

 

[bbl]

bbl, were you told that it has a vertical asymptote? Not all of those have vertical asymptotes. If the radicand
has no zeroes, then it has no vertical asymptotes. By the way, plotting it on WolframAlpha could be
misleading.

We were told to look for both horizontal and vertical asymptotes. I already found the horizontal asymptotes but I was having trouble looking for the vertical ones. But your response cleared things up! If I may ask, how can plotting it on WolframAlpha be misleading?

 

[lookagain]

If I may ask, how can plotting it on WolframAlpha be misleading?

I typed "plot (x - 9)/sqrt(4x^2 + 3x + 2)" in the space on WolframAlpha.
The graph they offer is shown cut off below the x-axis, and it looks like
it has a vertical asymptote. Go back and ask WolframAlpha for a minimum,
and it states $\displaystyle \ y \ge -12.$

 

[JeffM]

A vertical asymptote occurs in a rational function at values where the denominator is zero.

Is there any value of x where the denominator is zero?

We can determine this, as pka suggested, by using the quadratic formula to look for real zeroes of $4x^2 + 3x + 2$. The determinant is $3^2 - 4(4)(2) = 9 - 32 < 0.$ There are no real zeroes. Therefore there are no vertical asymptotes, whatever nonsense may seem to be implied by Wolfram.

 

[bbl]

A vertical asymptote occurs in a rational function at values where the denominator is zero.

Is there any value of x where the denominator is zero?

We can determine this, as pka suggested, by using the quadratic formula to look for real zeroes of $4x^2 + 3x + 2$. The determinant is $3^2 - 4(4)(2) = 9 - 32 < 0.$ There are no real zeroes. Therefore there are no vertical asymptotes, whatever nonsense may seem to be implied by Wolfram.

Thank you for your reply! I have a better understanding now