13. \( f(x)=\frac{2}{3} x^{2} \)

Did you know that functions like \( f(x)=\frac{2}{3} x^{2} \) are examples of quadratic functions? Quadratic functions are widely used in physics, economics, and various fields to model a variety of real-world scenarios, such as projectile motion or profit maximization. The parabolic shape of the graph indicates how the output changes as the input varies, allowing for easy visualization of maximum or minimum points! Now, if you're dealing with this quadratic function, a common mistake is forgetting to identify its vertex and intercepts. The vertex of this function, located at the origin (0,0), is the point where it changes direction. Make sure to use the vertex form when you're graphing or solving problems to avoid confusion—especially when the function gets more complex!