Linear and Quadratic Systems

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve a system of linear equations?

Back

You can use substitution, elimination, or graphing methods to find the values of the variables that satisfy both equations.

Front

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

Back

A point is a solution if it satisfies all equations in the system when substituted into them.

Front

What is the significance of the intersection point of two graphs?

Back

The intersection point represents the solution to the system of equations, where both equations are true.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is a system of inequalities?

Back

A set of inequalities that can be graphed on the same coordinate plane, representing a region of solutions.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality sign.

Front

What does it mean for a solution to be feasible in a system of inequalities?

Back

A feasible solution is one that satisfies all inequalities in the system.