1. The problem asks to find the value of the function $a(x) = 4x^2 + 2x - 5$ at $x = -2$. 2. To solve this, substitute $x = -2$ into the function: $$a(-2) = 4(-2)^2 + 2(-2) - 5$$ 3. Calculate each term step-by-step: $$4(-2)^2 = 4 \times 4 = 16$$ $$2(-2) = -4$$ 4. Now substitute these values back: $$a(-2) = 16 - 4 - 5$$ 5. Simplify the expression: $$16 - 4 - 5 = 12 - 5 = 7$$ 6. Therefore, the value of $a(-2)$ is $7$.