The function given is:

$h(t) = -16t^2 + 64t + 3$

To determine the restricted domain of the function, we must consider any constraints that may affect the values of $t$.

Step-by-Step Approach:

1. Quadratic Nature: The function is a quadratic (parabolic) expression, where the highest degree of $t$ is 2. Quadratic functions, like this one, are generally defined for all real numbers unless stated otherwise.

2. Physical Context (Optional): If this function represents a real-world scenario (e.g., projectile motion where $h(t)$ represents height and $t$ represents time), there could be restrictions. In such a case, $t \geq 0$ would be required, because negative time does not make physical sense.

3. Domain: If no explicit restriction is given, the domain of a quadratic function like this is all real numbers. However, for real-world problems like motion, we typically restrict the domain to non-negative values of $t$, as time can’t be negative.

Thus, the restricted domain might be:

$t \geq 0$

Do you have more information about the context of this function? That could help confirm if there are physical constraints that we need to apply.

Would you like me to explain this further? Here are some related questions that could expand your understanding:

1. How do you find the vertex of a quadratic function?
2. How do you determine the range of this function?
3. What real-world problems could this quadratic function model?
4. How do you solve for when $h(t) = 0$ (i.e., when the function reaches ground level)?
5. What is the significance of the coefficient $-16$ in this function?

Tip: Quadratic functions usually have all real numbers as their domain unless there are specific physical or problem constraints.