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 when graphed.

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

Back

By finding the points of intersection between the linear and quadratic graphs; the number of intersection points indicates the number of solutions.

Front

What does it mean if a system has no solutions?

Back

It means the graphs of the equations do not intersect, indicating that there are no common 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 do you solve a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the points where they intersect.

Front

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

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.

Front

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

Back

By substituting the linear equation into the quadratic equation and solving for the variable.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is U-shaped and can open upwards or downwards.