1. The problem is to find the axis of symmetry for the quadratic function $-2x^2 + 6x - 3$. 2. The axis of symmetry for a quadratic function in the form $ax^2 + bx + c$ is given by the formula: $$x = -\frac{b}{2a}$$ 3. Here, $a = -2$ and $b = 6$. Substitute these values into the formula: $$x = -\frac{6}{2 \times (-2)}$$ 4. Simplify the denominator: $$x = -\frac{6}{-4}$$ 5. Simplify the fraction: $$x = \frac{6}{4} = \frac{3}{2}$$ 6. Therefore, the axis of symmetry is the vertical line: $$x = \frac{3}{2}$$ This line divides the parabola into two symmetric halves.