1. **State the problem:** We need to find the value of the composite function $(f \circ g)(-3)$, which means $f(g(-3))$. 2. **Recall the definitions:** - $f(x) = 2x^2 - 4x + 7$ - $g(x) = -4x - 15$ 3. **Find $g(-3)$:** Substitute $-3$ into $g(x)$: $$g(-3) = -4(-3) - 15 = 12 - 15 = -3$$ 4. **Find $f(g(-3)) = f(-3)$:** Substitute $-3$ into $f(x)$: $$f(-3) = 2(-3)^2 - 4(-3) + 7 = 2(9) + 12 + 7 = 18 + 12 + 7 = 37$$ 5. **Final answer:** $$(f \circ g)(-3) = 37$$