(f) \( 21 x^{2}+11 x-2 \)

Did you know that the quadratic equation \(21 x^{2}+11 x-2\) can be factored or solved using the quadratic formula? Factoring polynomials can be quite a puzzle, but finding its roots can help in graphing or understanding the curve’s behavior. You can visualize it like finding the x's where the parabola dips below or rises above the x-axis! If you're interested in practical applications, quadratic equations like this one frequently pop up in physics, especially in trajectories of projectiles. Understanding how to manipulate and solve these equations is essential for predicting motion and analyzing real-world phenomena—making them not just classroom exercises, but vital tools for engineers, architects, and more!