Answer: A. The toy car's minimum height was $5$ inches above the ground.

Explanation:1. Identify the given function: $f(x) = \dfrac{1}{9}(x-4)^2 + 5$, where $f(x)$ is the toy car's height in inches, and $x$ is the time in seconds after it started moving, for $0 \le x \le 10$.

2. Recognize the form of the function: The function is a quadratic function in vertex form, $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex of the parabola. In this case, $a = \dfrac{1}{9}$, $h = 4$, and $k = 5$.

3. Determine the vertex: The vertex of the graph of $y=f(x)$ is at $(h, k) = (4, 5)$.

4. Interpret the vertex in the context of the problem: - The $x$-coordinate of the vertex, $h=4$, represents the time in seconds when the extremum height occurs. - The $y$-coordinate of the vertex, $k=5$, represents that extremum height in inches. - Since the coefficient $a = \dfrac{1}{9}$ is positive ($a > 0$), the parabola opens upwards, meaning the vertex represents a minimum point. - Therefore, the minimum height of the toy car is $5$ inches, and this occurs at $x=4$ seconds.

5. Evaluate the given options based on this interpretation: - [A] The toy car's minimum height was $5$ inches above the ground. (This matches our interpretation of $k=5$ as the minimum height). - [B] The toy car's minimum height was $4$ inches above the ground. (Incorrect, $4$ is the time when the minimum height occurs). - [C] The toy car's height was $5$ inches above the ground when it started moving. (When it started moving, $x=0$. $f(0) = \dfrac{1}{9}(0-4)^2 + 5 = \dfrac{1}{9}(-4)^2 + 5 = \dfrac{1}{9}(16) + 5 = \dfrac{16}{9} + 5 \neq 5$). - [D] The toy car's height was $4$ inches above the ground when it started moving. (Incorrect, based on calculation for $f(0)$ and interpretation of $4$).

6. Conclusion: The best interpretation of the vertex is that the toy car's minimum height was $5$ inches above the ground.