The equation in the image is:

$y = x^2 + 2|x|$

This equation combines two components:

1. $x^2$: a parabolic term that is always non-negative.
2. $2|x|$: an absolute value term multiplied by 2, which ensures symmetry about the $y$-axis and adds a linear effect.

Key Observations:

1. Symmetry: The function is symmetric about the $y$-axis because both $x^2$ and $|x|$ are even functions.
2. Shape of the graph:
   • For $x \geq 0$, $|x| = x$, so the equation simplifies to $y = x^2 + 2x$.
   • For $x < 0$, $|x| = -x$, so the equation simplifies to $y = x^2 - 2x$.
3. Smoothness: The graph will have no breaks but will show a “bend” where $x = 0$ due to the absolute value term.

Would you like me to graph this equation or explain further details? Here are some additional related questions for you:

1. What does the symmetry about the $y$-axis imply?
2. How does the absolute value term $|x|$ influence the graph’s behavior?
3. How can we determine the vertex of this graph?
4. What are the differences between this graph and the standard parabola $y = x^2$?
5. How would you sketch this function step by step?

Tip: Remember that the absolute value function causes changes in slope depending on the sign of $x$.