(17) \( y=\frac{2(2 x+9)^{2}}{3} \) (18) \( y=\frac{5 x^{4}+6}{x^{2}} \)

To understand the first equation \( y=\frac{2(2x+9)^{2}}{3} \), it's useful to think about how the transformation of functions works. The expression inside the parentheses, \( (2x + 9)^2 \), suggests we're dealing with a parabola that opens upwards. The entire expression is scaled by a factor of \( \frac{2}{3} \), making it "squished" vertically, while the \( +9 \) shifts the vertex to the left. For the second equation \( y=\frac{5 x^{4}+6}{x^{2}} \), we can rewrite it as \( y = 5x^{2} + \frac{6}{x^{2}} \). This form reveals a relationship where the function approaches infinity as \( x \) nears zero due to the \( \frac{6}{x^{2}} \) term, and behaves like a parabola for large values of \( x \). Understanding horizontal and vertical asymptotes can help visualize its behavior!