Ruutfunktsioon

Ruutfunktsioon is the Finnish term for a quadratic function. A quadratic function is a polynomial function of degree two, meaning it can be written in the general form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to zero. The graph of a ruutfunktsioon is a parabola. The shape and orientation of the parabola are determined by the coefficients a, b, and c. If a is positive, the parabola opens upwards, and if a is negative, it opens downwards. The coefficient b influences the position of the axis of symmetry, and the constant c represents the y-intercept, the point where the parabola crosses the y-axis.

The roots of a ruutfunktsioon, also known as its zeros, are the x-values for which f(x) = 0. These are the points where the parabola intersects the x-axis. The roots can be found using the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a. The discriminant, b^2 - 4ac, determines the nature of the roots. If the discriminant is positive, there are two distinct real roots. If it is zero, there is exactly one real root (a repeated root). If it is negative, there are no real roots, but two complex conjugate roots. Ruutfunktsioonid have numerous applications in various fields, including physics, engineering, and economics, for modeling projectile motion, optimization problems, and cost analysis.