To find the vertical asymptotes of the function:

$y = \frac{3x^2}{x^2 - 25}$

we look for the values of $x$ that make the denominator zero, because a vertical asymptote occurs where the function tends to infinity due to division by zero.

Step 1: Set the denominator equal to zero.

$x^2 - 25 = 0$

Step 2: Solve for $x$.

$x^2 = 25$ $x = \pm 5$

Conclusion:

The vertical asymptotes occur at $x = 5$ and $x = -5$.

Would you like more details on vertical asymptotes, or do you have any questions?

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Here are 5 related questions:

1. How can you find horizontal asymptotes of the same function?
2. What is the domain of this function?
3. How do you graph a rational function with asymptotes?
4. How do you determine slant (oblique) asymptotes?
5. What happens to the graph near the vertical asymptotes?

Tip: When solving rational functions, always check both the numerator and the denominator for simplifications before finding asymptotes!