Determine the vertical asymptote(s) of the graph of the function.
-$$f ( a ) = \frac { a ^ { 2 } + 4 } { a ^ { 2 } + 3 a - 5 }$$
A) $a = \frac { - 3 + \sqrt { 29 } } { 2 }$ and $a = \frac { - 3 - \sqrt { 29 } } { 2 }$
B) $a = 2$ and $a = - 2$
C) $a = - \frac { 5 } { 3 }$
D) None

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (assuming the numerator is not zero at the same point, which would indicate a hole instead). For the given function, $\frac { a ^ { 2 } + 4 } { a ^ { 2 } + 3 a - 5 }$, we find the vertical asymptotes by setting the denominator equal to zero and solving for $a$: $a^2 + 3a - 5 = 0$. Solving this quadratic equation using the quadratic formula, $a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = 3$, and $c = -5$, gives $a = \frac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} = \frac{-3 \pm \sqrt{9 + 20}}{2} = \frac{-3 \pm \sqrt{29}}{2}$.

Determine the Vertical Asymptote(s) of the Graph of the Function f(a)=a2+4a2+3a−5f ( a ) = \frac { a ^ { 2 } + 4 } { a ^ { 2 } + 3 a - 5 }f(a)=a2+3a−5a2+4​

Determine the Vertical Asymptote(s) of the Graph of the Function $f ( a ) = \frac { a ^ { 2 } + 4 } { a ^ { 2 } + 3 a - 5 }$