Nonlinear Systems

Front

What is a nonlinear system?

Back

A nonlinear system is a system of equations in which at least one equation is not linear, meaning it cannot be represented as a straight line on a graph.

Front

What is the general form of a quadratic equation?

Back

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

Front

How do you find the intersection of two equations graphically?

Back

To find the intersection of two equations graphically, plot both equations on the same graph and identify the points where they cross.

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the graphs of the equations do not intersect, indicating that there are no common points.

Front

What is the solution to the system: y = x² + 3x - 5 and y = x + 3?

Back

The solutions are (-4, -1) and (2, 5).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, representing the maximum or minimum value of the function.

Front

How can you determine the number of solutions in a nonlinear system?

Back

The number of solutions can be determined by analyzing the graphs of the equations: they can intersect at zero, one, or two points.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

What does it mean for a system to be consistent?

Back

A consistent system of equations has at least one solution, meaning the graphs of the equations intersect at one or more points.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.