Non-Linear Systems

Front

What is a non-linear system?

Back

A non-linear system is a system of equations where at least one equation is not linear, 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 of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola given by y = ax² + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate.

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a smooth curve through them.

Front

What is the method of substitution in solving systems of equations?

Back

The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the method of elimination in solving systems of equations?

Back

The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How can you determine if two equations intersect?

Back

Two equations intersect if their graphs meet at one or more points, which corresponds to the solutions of the system of equations.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape, which opens upwards if a > 0 and downwards if a < 0.