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 expressed in the form y = mx + b.

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

How do you find the intersection of two curves?

Back

To find the intersection of two curves, set the equations equal to each other and solve for the variable.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

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 is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if it has at least one solution.

Front

What is a solution set?

Back

A solution set is the set of all possible solutions to a system of equations.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot points to form a parabola.