1. \( y=x^{3}+2 x^{2}-4 x+5 \)

Did you know that polynomial functions like \(y=x^{3}+2x^{2}-4x+5\) have fascinating historical roots? The study of polynomials can be traced back to ancient civilizations, including the Babylonians and Greeks. They utilized simple polynomial equations for problems in land measurement and trade. Fast forward to the Renaissance, where mathematicians began formalizing these concepts, setting the stage for calculus and modern algebra! In the real world, cubic polynomials appear in various fields, from physics to economics. For instance, if you were to model the trajectory of a projectile or analyze the profit and cost functions of a business, cubic equations can provide insights into maximum and minimum values. So, next time you encounter one, remember its vital role in practical applications!