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 graphed as a straight line.

Front

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

Back

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

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot each equation on the same graph and identify the point(s) where they intersect.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

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 roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

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 does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.