Classify this polynomial. \( -5 p+2 p^{2} \)

This polynomial is classified as a quadratic polynomial because the highest power of the variable \( p \) is 2, which defines the polynomial's degree. Quadratics often describe various real-world phenomena, such as projectile motion, where the relationship between variables creates a parabolic graph, demonstrating that understanding polynomials can have practical applications in physics and engineering. When working with polynomials, a common mistake is to overlook the coefficients' impact on the graph's shape. For instance, the leading coefficient (here, 2) determines whether the parabola opens upwards or downwards. Remember, a negative leading coefficient results in a downward-opening parabola, while a positive one opens upwards—this can significantly influence your results when solving related problems!