The axis of symmetry for the quadratic equation

$y = -x^2 + 4x - 3$

is given by the line

$x = 2.$

To determine the axis of symmetry for a quadratic equation in the standard form

$y = ax^2 + bx + c,$

you can utilize the formula

$x = -\frac{b}{2a}.$

In our specific equation, the coefficients are $a = -1$, $b = 4$, and $c = -3$. By substituting these values into the formula, we have:

$x = -\frac{4}{2(-1)} = -\frac{4}{-2} = 2.$

Thus, the axis of symmetry is represented by the vertical line

$x = 2.$

The axis of symmetry is a crucial line that divides the parabola into two mirror-image halves. In this case, the parabola opens downwards because the coefficient of $x^2$, which is $a$, is negative. The vertex of the parabola, which is the highest point in this scenario, lies on the axis of symmetry. Therefore, if you were to fold the graph along the line $x = 2$, both sides of the parabola would align perfectly.

Understanding the axis of symmetry is essential, as it aids in sketching the graph of the quadratic function and locating the vertex. For the equation

$y = -x^2 + 4x - 3,$

the vertex can be found by substituting $x = 2$ back into the equation to calculate the corresponding y-coordinate:

$y = - (2)^2 + 4(2) - 3 = -4 + 8 - 3 = 1.$

Consequently, the vertex is located at the point

$(2, 1),$

confirming that the axis of symmetry is

$x = 2.$