Find the Domain y=a(x-h)^2+k

Problem

y=a*(x−h)^2+k

Solution

1. Identify the type of function given. The expression y=a*(x−h)^2+k is a quadratic function written in vertex form.

2. Determine the constraints on the input variable x A quadratic function is a polynomial of degree 2.

3. Analyze the operations involved. The expression involves subtraction, squaring, and multiplication by constants. These operations are defined for all real numbers.

4. Conclude that there are no values of x that would result in division by zero or the square root of a negative number. Therefore, the domain consists of all real numbers.

Final Answer

Domain:(−∞,∞)

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