Parabola with absolute value

Consider the graph of $y = |x^2 - 1|$. It is the parabola $y = x^2 - 1$ with the part below the $x$-axis (for $-1 < x < 1$) folded upward across the $x$-axis.

At $x = -1, 1$, where $x^2 - 1 = 0$, the graph meets the $x$-axis with a corner, and in between it becomes $y = 1 - x^2$ with a peak at $(0, 1)$. For $|x| \ge 1$ it stays as the original $y = x^2 - 1$. The large dots mark the corners $(-1, 0)$, $(1, 0)$ and the peak $(0, 1)$.