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We are given the function \( f(x) = -2x^2 + 7 \) and the domain \( D = \{2, -3, 0\} \). Our goal is to find the range, which means we need to calculate the values of \( f(x) \) for each \( x \) in the domain.

1. For \( x = 2 \):
   \[
   f(2) = -2(2^2) + 7 = -2(4) + 7 = -8 + 7 = -1
   \]

2. For \( x = -3 \):
   \[
   f(-3) = -2((-3)^2) + 7 = -2(9) + 7 = -18 + 7 = -11
   \]

3. For \( x = 0 \):
   \[
   f(0) = -2(0^2) + 7 = -2(0) + 7 = 7
   \]

Thus, the range \( R \) is the set of the function values: \( R = \{-1, -11, 7\} \).

Do you want more details or have any questions?

Here are some related questions:
1. How does changing the coefficient of \( x^2 \) affect the range of a quadratic function?
2. What is the significance of the vertex in determining the range of a quadratic function?
3. How do you find the domain and range for more complex functions, such as those involving square roots or logarithms?
4. Can a quadratic function ever have a maximum range value instead of a minimum?
5. What are the differences between the domain and range in linear versus quadratic functions?

**Tip:** When working with quadratic functions, the direction of the parabola (opening up or down) is determined by the sign of the coefficient of \( x^2 \).

Use the given domain to find the range of the following function: f(x) = -2x^2 + 7, D = {2, -3, 0}.

This problem involves finding the range of the quadratic function f(x) = -2x^2 + 7 for the domain D = {2, -3, 0}. It covers key concepts in algebra and quadratic functions, making it suitable for students in Grades 8-10.

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