1. **State the problem:** We want to find and simplify $a(x-2)$ where $a(x) = 4x^{2} + 2x - 5$. 2. **Recall the function substitution:** $a(x-2) = 4(x-2)^{2} + 2(x-2) - 5$ 3. **Expand the squared term:** $(x-2)^{2} = x^{2} - 2 \times 2 \times x + 2^{2} = x^{2} - 4x + 4$ 4. **Substitute back and expand:** $a(x-2) = 4(x^{2} - 4x + 4) + 2(x-2) - 5$ $= 4x^{2} - 16x + 16 + 2x - 4 - 5$ 5. **Combine like terms:** $= 4x^{2} - 16x + 2x + 16 - 4 - 5$ $= 4x^{2} - 14x + 7$ 6. **Final simplified expression:** $$a(x-2) = 4x^{2} - 14x + 7$$