1. **State the problem:** Find the equation of the axis of symmetry for the parabola given by $$y = 4x^2 + 16x + 32$$. 2. **Formula:** The axis of symmetry for a parabola in the form $$y = ax^2 + bx + c$$ is given by $$x = -\frac{b}{2a}$$. 3. **Identify coefficients:** Here, $$a = 4$$ and $$b = 16$$. 4. **Substitute values:** $$x = -\frac{16}{2 \times 4}$$ 5. **Simplify denominator:** $$x = -\frac{16}{\cancel{2} \times \cancel{4}}$$ $$x = -\frac{16}{8}$$ 6. **Simplify fraction:** $$x = -2$$ 7. **Conclusion:** The equation of the axis of symmetry is $$x = -2$$. This vertical line passes through the vertex of the parabola and divides it into two symmetric halves.