Non-Linear Systems

Front

What is a non-linear system?

Back

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.

Front

What is the general form of a quadratic equation?

Back

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

Front

How do you find the vertex of a quadratic function?

Back

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

Front

What does the discriminant of a quadratic equation tell us?

Back

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.

Front

What is the difference between linear and non-linear functions?

Back

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.

Front

How do you solve a system of equations graphically?

Back

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.

Front

What is the significance of the intersection points in a non-linear system?

Back

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

Front

What is a linear-quadratic system?

Back

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

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

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