Find the Domain h=-16t^2+45t+6

Problem

h=−16*t2+45*t+6

Solution

1. Identify the type of function. The given expression h=−16*t2+45*t+6 is a polynomial function of degree 2, also known as a quadratic function.

2. Determine the mathematical domain. For any polynomial function, there are no square roots of negative numbers and no divisions by zero. Therefore, the function is defined for all real numbers.

3. Consider the physical context. In physics, the variable t usually represents time and h represents height. In such cases, the domain is often restricted to t≥0 and ends when the object hits the ground (h=0.

4. State the general mathematical domain. Unless a specific physical context is provided requiring h≥0 the domain of a quadratic polynomial is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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