Nonlinear Systems of Equations & Inequalities

Front

What is a nonlinear system of equations?

Back

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

Front

What does it mean if two graphs have no points of intersection?

Back

If two graphs have no points of intersection, it means that the system of equations has no solutions.

Front

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

Back

The number of solutions can be determined by analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they intersect at two points, there are two solutions; if they are parallel, there are no solutions; if they are the same line, there are infinite solutions.

Front

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

Back

The vertex of a quadratic equation represents the maximum or minimum point of the parabola, which is crucial for understanding the graph's behavior.

Front

What is the standard form of a quadratic equation?

Back

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

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 have infinite solutions?

Back

A system has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve.

Front

What is the difference between linear and nonlinear equations?

Back

Linear equations graph as straight lines and have a constant rate of change, while nonlinear equations graph as curves and have varying rates of change.

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values that satisfy all equations in the system simultaneously.