1. **State the problem:** We need to find the value of the function $f(x) = 3x^2 - 5$ at $x = -2$. 2. **Recall the formula:** The function is given by $$f(x) = 3x^2 - 5$$ 3. **Substitute $x = -2$ into the function:** $$f(-2) = 3(-2)^2 - 5$$ 4. **Calculate the square:** $$(-2)^2 = 4$$ So, $$f(-2) = 3 \times 4 - 5$$ 5. **Multiply:** $$3 \times 4 = 12$$ So, $$f(-2) = 12 - 5$$ 6. **Subtract:** $$12 - 5 = 7$$ **Final answer:** $$f(-2) = 7$$