Linear/Quadratic Systems of Equations (YL Flashcard)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has no solutions?

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has two solutions?

Back

This occurs in a quadratic-linear system where the quadratic curve intersects the line at two points.

Tags

CCSS.HSA.REI.C.7

Front

What is a quadratic equation?

Back

An equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By analyzing the intersection points of the graphs of the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point on the graph of the quadratic function, depending on its orientation.

Front

What is the discriminant in a quadratic equation?

Back

The value calculated as b² - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate?

Back

There are two distinct real solutions to the quadratic equation.

Tags

CCSS.HSA-REI.B.4B