Passage: Consider the curves y=x^2 and y=2|x| . Question: What is...

Equating the two given curves $y = x^2$ and $y = 2|x|$:

$x^2 = 2|x|$

Since $x^2 = |x|^2$, the equation becomes:

$|x|^2 - 2|x| = 0$

$|x|(|x| - 2) = 0$

This gives $|x| = 0$ or $|x| = 2$.

Solving for $x$, we get $x = 0$, $x = 2$, and $x = -2$.

The corresponding points of intersection are $(0,0)$, $(2,4)$, and $(-2,4)$.

The number of points of intersection is $3$.

Answer: $3$