Final answer:
Quadratic functions are second-order polynomials. To solve a quadratic equation, set the function equal to zero, and use the quadratic formula. The corresponding polynomial function in this case is f(x) = x² + 5x - 1.
Step-by-step explanation:
The Solution of Quadratic Equations
Quadratic functions are second-order polynomials. They are of the form f(x) = ax² + bx + c, where a, b, and c are constants. To solve a quadratic equation, set the function equal to zero, and use the quadratic formula: x = (-b ± √(b²-4ac))/(2a). The discriminant, b²-4ac, determines the number and nature of the solutions. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution (a perfect square). If it is negative, there are no real solutions, but there are two complex solutions.
In this case, the corresponding polynomial function is f(x) = x² + 5x - 1.