# How do you find the domain and range for #y = -.566021616 (x - 6) ^2 + 3.7#?

See below.

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To find the domain and range of the function y = -0.566021616(x - 6)^2 + 3.7:

Domain: The domain of the function is all real numbers since there are no restrictions on the input variable x.

Range: To find the range, analyze the behavior of the quadratic function. Since the coefficient of the squared term is negative, the parabola opens downwards. The vertex of the parabola is at (6, 3.7). The maximum value of the function occurs at the vertex, so the range is all real numbers less than or equal to the y-coordinate of the vertex. Therefore, the range is y ≤ 3.7.

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