Final answer:
The end behavior of the polynomial -5x⁵+7x⁴-6x³+4x²+6 is determined by its leading term -5x⁵, indicating that as x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity.
Step-by-step explanation:
The student's question seems to focus on determining the end behavior of the polynomial -5x⁵+7x´-6x³+4x²+6. To analyze end behavior, one must look at the leading term, which is the term with the highest power of x. In this case, the leading term is -5x⁵. The coefficient is negative, and the degree is odd, indicating that as x → -∞, f(x) → ∞ and as x → ∞, f(x) → -∞. When eliminating terms to simplify the algebra, we cannot eliminate any terms for determining end behavior as each term contributes to the polynomial's shape. To ensure the reasonableness of the answer, one should check that the power and coefficient of the leading term are correctly identified. The quadratic formula, which is not applicable here, is generally used for solving equations of the form ax² + bx + c = 0.