Analyze the curve $y = \frac{x}{x^2 - 1}$ for symmetry, intercepts, asymptotes, and sketch its behavior.

Analyze and sketch the parabolic curve $y = -x^2 + 4x - 3$ by determining: (a) Direction of concavity (b) Coordinates of the vertex and axis of symmetry (c) $x$-intercepts and $y$-intercept (d) Maximum value and range of the function