1. **State the problem:** Find the value of $z$ at the point $(2,-1)$ for the function $z = 3y^2 - 2x^2 + x$. 2. **Recall the formula:** The function is given by $$z = 3y^2 - 2x^2 + x$$ where $x=2$ and $y=-1$. 3. **Substitute the values:** $$z = 3(-1)^2 - 2(2)^2 + 2$$ 4. **Calculate powers:** $$z = 3(1) - 2(4) + 2$$ 5. **Simplify terms:** $$z = 3 - 8 + 2$$ 6. **Perform addition and subtraction:** $$z = (3 + 2) - 8 = 5 - 8 = -3$$ **Final answer:** $$z = -3$$