1. **State the problem:** We are given parametric equations \(x = t^2 + 1\), \(y = 4t - 3\), and \(z = 2(t^2 - 3t)\) and need to find the values of \(x\), \(y\), and \(z\) at \(t = 0\). 2. **Recall the formula:** To find the position on the curve at a specific parameter value, substitute \(t = 0\) into each equation. 3. **Calculate each coordinate:** - \(x = (0)^2 + 1 = 0 + 1 = 1\) - \(y = 4(0) - 3 = 0 - 3 = -3\) - \(z = 2((0)^2 - 3(0)) = 2(0 - 0) = 0\) 4. **Interpretation:** At \(t = 0\), the point on the curve is \((x, y, z) = (1, -3, 0)\). **Final answer:** \(\boxed{(1, -3, 0)}\)