A quadratic polynomial is a function of the form P(x) = ax^2 + bx + c, where a, b, and c are constants, and a is not equal to zero. It is a second-degree polynomial, which means it has a degree of 2, indicating that the highest power of the variable, x, is 2.
The term "quadratic" derives from the Latin word "quadratus," which means square. This is because the highest power term in a quadratic polynomial is a squared term (x^2), while the other terms (bx and c) are linear.
Quadratic polynomials have various applications in different fields, such as physics, engineering, economics, and computer science. They are commonly used to model real-world phenomena, especially those that involve squares or areas, such as projectile motion, parabolic trajectories, and geometric problems.
The graph of a quadratic polynomial is a curve called a parabola. The shape and orientation of the parabola depend on the coefficient a. If a is positive, the parabola opens upwards, resembling a "U" shape, while if a is negative, the parabola opens downwards, resembling an inverted "U" shape. The vertex of the parabola, which represents the minimum or maximum point of the quadratic polynomial, can be determined by the formula x = -b/2a. The zeros or roots of the quadratic polynomial, indicating the values of x for which P(x) equals zero, can be obtained by factoring, completing the square, or using the quadratic formula.
