10) \( 4 x^{2}+9 x+2 \)

Did you know that the quadratic expression \(4x^{2} + 9x + 2\) can be understood in the context of its roots? By using the quadratic formula, \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\), you’ll find the values of \(x\) where the expression equals zero. For \(a = 4\), \(b = 9\), and \(c = 2\), this expression has real roots revealing more about its behavior on the graph! Want to apply your newfound knowledge? You can use this quadratic in real-life scenarios, like modeling projectile motion or determining optimal pricing in a business. Plotting this expression on a graph will illustrate its parabolic shape, showcasing maximum or minimum points, which can be fascinating to analyze as they represent real-world trajectories or cost functions!