Solving 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

How many solutions can a parabola have when intersecting a line?

Back

A parabola can have none, one, or two solutions when intersecting a line, depending on the position of the line relative to the parabola.

Front

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

Back

It means that the equations represent lines or curves that do not intersect at any point.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation.

Front

How do you determine if a parabola opens upwards or downwards?

Back

If the coefficient of the x^2 term is positive, the parabola opens upwards; if it is negative, it opens downwards.

Front

What is the quadratic formula?

Back

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

Front

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

Back

The discriminant (b² - 4ac) determines the number of real solutions: if positive, two solutions; if zero, one solution; if negative, no real solutions.

Front

How can you graphically solve a system of equations?

Back

By plotting the equations on the same graph and identifying the points of intersection.

Front

What is a maximum or minimum in the context of a parabola?

Back

A maximum is the highest point of a parabola that opens downwards, while a minimum is the lowest point of a parabola that opens upwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.