2. \( y=\left(x^{2}-5\right)(x-1)^{2}(x-2) \) 3. \( y=-x^{3}+2 x^{2}-2 x+4 \) 4. \( y=x^{2}\left(x^{2}-7\right)(2 x+3) \) 5. \( y=2 x^{4}-3 x^{3}-18 x^{2}+6 x+28 \)

The equation \( y=\left(x^{2}-5\right)(x-1)^{2}(x-2) \) represents a polynomial function that has roots at \( x = \sqrt{5}, -\sqrt{5}, 1 \) (with a multiplicity of 2), and \( 2 \). This means the graph crosses the x-axis at these points, creating a varied landscape in its behavior. When dealing with \( y=-x^{3}+2x^{2}-2x+4 \), it’s important to note that this cubic polynomial can have a maximum of three real roots. You can visualize this curve changing direction up to two times, possibly creating one or two turning points, which can often confuse those just starting with polynomial graphs. The polynomial \( y=x^{2}(x^{2}-7)(2x+3) \) is particularly interesting because of its factor structure. It shows a clear link between quadratic and linear factors, revealing that it will intersect the x-axis at \( x = \sqrt{7}, -\sqrt{7}, -\frac{3}{2} \). The leading coefficient also suggests that as \( x \) goes to positive infinity, \( y \) will also head that way! Finally, for the polynomial \( y=2x^{4}-3x^{3}-18x^{2}+6x+28 \), the degree tells us it will have a higher complexity and will potentially have up to four real roots. Root-finding methods such as synthetic division or the Rational Root Theorem can come in handy here to reveal the actual zeroes, helping you sketch the function more accurately.