Solving Systems of linear and quadratic equations

Front

What is a system of linear and quadratic equations?

Back

A system of linear and quadratic equations consists of at least one linear equation and one quadratic equation, and the solutions are the points where their graphs intersect.

Tags

CCSS.HSA.REI.C.7

Front

How many solutions can a linear-quadratic system have?

Back

A linear-quadratic system can have 0, 1, or 2 solutions depending on the position of the graphs.

Tags

CCSS.HSA.REI.C.7

Front

What does it mean if a system has 0 solutions?

Back

It means that the graphs of the equations do not intersect at any point.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if a system has 1 solution?

Back

It means that the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system has 2 solutions?

Back

It means that the graphs of the equations intersect at two distinct points.

Tags

CCSS.8.EE.C.8B

Front

How can you determine the number of solutions graphically?

Back

By graphing both equations and observing the points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The solution is the set of values that satisfy all equations in the system.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

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

Back

The vertex is the highest or lowest point of the parabola, which can indicate the maximum or minimum value of the quadratic function.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the difference between linear and quadratic equations?

Back

Linear equations represent straight lines and have a degree of 1, while quadratic equations represent parabolas and have a degree of 2.