MPM2D1-6; P. Athanassenas Final Exam Part 2 - June 2023 6. A cat jumps off a fence. The equation $h=-0.5 d^{2}+d+2$ describes the height $\boldsymbol{h}$ of the cat at a distance $\boldsymbol{d}$ from the fence. a) How far from the fence will the cat land on the ground?

Step 1 ：Given the equation \(h = -0.5d^2 + d + 2\), we need to find the value of \(d\) when \(h = 0\).

Step 2 ：Set the equation to 0: \(0 = -0.5d^2 + d + 2\).

Step 3 ：Solve the quadratic equation for \(d\).

Step 4 ：The solutions for \(d\) are approximately -1.24 and 3.24.

Step 5 ：Since distance cannot be negative, the cat will land on the ground \(\boxed{3.24}\) units away from the fence.