What is the axis of symmetry for y = -x^2 + 4x - 3?

The axis of symmetry for the quadratic equation \( y = -x^2 + 4x - 3 \) is \( x = 2 \).

To find the axis of symmetry for a quadratic equation in the form \( y = ax^2 + bx + c \), you can use the formula \( x = -\frac{b}{2a} \). In this equation, \( a = -1 \), \( b = 4 \), and \( c = -3 \). Plugging these values into the formula gives:

\[ x = -\frac{4}{2(-1)} = -\frac{4}{-2} = 2 \]

So, the axis of symmetry is the vertical line \( x = 2 \).

The axis of symmetry is a line that divides the parabola into two mirror-image halves. For the given quadratic equation, 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 case, lies on the axis of symmetry. This means that if you were to fold the graph along the line \( x = 2 \), both sides of the parabola would match perfectly.

Understanding the axis of symmetry is crucial because it helps in sketching the graph of the quadratic function and finding the vertex. For \( y = -x^2 + 4x - 3 \), the vertex can be found by substituting \( x = 2 \) back into the equation to get the y-coordinate. This gives:

\[ y = -(2)^2 + 4(2) - 3 = -4 + 8 - 3 = 1 \]

So, the vertex is at \( (2, 1) \), and the axis of symmetry is \( x = 2 \).