Nonlinear Systems of Equations

Front

What is a nonlinear system of equations?

Back

A system of equations where at least one equation is nonlinear, 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 is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the intersection of a linear and a quadratic equation?

Back

Set the equations equal to each other and solve for the variable, then substitute back to find the corresponding value.

Front

What does it mean if a nonlinear system has no solutions?

Back

It means the graphs of the equations do not intersect at any point.

Front

What does it mean if a nonlinear system has one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

What does it mean if a nonlinear system has two solutions?

Back

It means the graphs of the equations intersect at two distinct points.

Front

What is the vertex of a parabola?

Back

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

Front

How can you determine the number of solutions in a linear-quadratic system?

Back

By analyzing the graphs of the equations or using the discriminant of the quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots.

Front

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

Back

The vertex form is y = a(x-h)² + k, where (h, k) is the vertex, making it easy to graph.