2.) \( \frac{3}{2} x^{2}-5 \)

This quadratic expression, \( \frac{3}{2} x^{2} - 5 \), is a perfect example of a parabolic function in mathematics. To visualize it, imagine a U-shaped curve opening upwards due to the positive coefficient \( \frac{3}{2} \) in front of \( x^{2} \). At \( x = 0 \), the value is -5, which means the vertex (the lowest point) is located at the point (0, -5) on the graph. One common mistake when working with quadratics is forgetting to factor or analyze them correctly. For instance, people often overlook finding the x-intercepts or the vertex because they jump straight to factoring or applying the quadratic formula. Always remember to check if a quadratic can be simplified or rephrased into vertex form for easier graphing!