Non-Linear Systems

A non-linear system is a system of equations in which at least one equation is not linear, meaning it cannot be expressed in the form y = mx + b.

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

The vertex of a quadratic function in the form y = ax² + bx + c can be found using the formula x = -b/(2a).

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Linear functions have a constant rate of change and graph as straight lines, while non-linear functions have varying rates of change and can graph as curves.

To solve a system of equations graphically, plot both equations on the same graph and identify the points where they intersect, which represent the solutions.

The intersection points of a non-linear system represent the solutions to the system, where the values satisfy all equations involved.

A linear-quadratic system consists of one linear equation and one quadratic equation, which can be solved simultaneously to find their intersection points.

A quadratic function opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

The axis of symmetry of a quadratic function in the form y = ax² + bx + c is the vertical line x = -b/(2a).