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 $x^2$.