1. **State the problem:** We are given the vector function $$\vec{y} = (x - 2)(x + 1)z$$ and need to understand or analyze it. 2. **Understand the expression:** The function involves variables $x$ and $z$, and the expression $(x - 2)(x + 1)$ is a quadratic polynomial in $x$. 3. **Expand the polynomial:** Use the distributive property: $$ (x - 2)(x + 1) = x^2 + x - 2x - 2 = x^2 - x - 2 $$ 4. **Rewrite the vector function:** $$ \vec{y} = (x^2 - x - 2) z $$ 5. **Interpretation:** This means the vector $\vec{y}$ depends on both $x$ and $z$, scaled by the quadratic polynomial in $x$. 6. **If graphing is intended:** The function can be seen as $y = (x^2 - x - 2) z$, which is a surface in 3D space depending on $x$ and $z$. 7. **Summary:** The key step is expanding the polynomial to understand the function's form. Final answer: $$ \vec{y} = (x^2 - x - 2) z $$