Find the Domain h=-16t^2+16

Problem

h=−16*t2+16

Solution

1. Identify the type of function. The expression h=−16*t2+16 is a polynomial function (specifically a quadratic).

2. Determine the mathematical domain. For any polynomial function, the variable t can be any real number because there are no square roots of negative numbers or divisions by zero.

3. Consider the physical context. In physics, h often represents height and t represents time. If t represents time starting from t=0 the domain is restricted to t≥0

4. Find the interval where height is non-negative. Set h≥0 to find when the object is at or above ground level.

−16*t2+16≥0

5. Solve the inequality for t

16≥16*t2

1≥t2

−1≤t≤1

6. Combine the constraints. For a physical trajectory starting at t=0 the domain is 0≤t≤1 In a pure mathematical context, the domain is all real numbers.

Final Answer

Domain: *{[t∈ℝ,0≤t≤1]}

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