Solving Systems of linear and quadratic equations

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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 that are solved together to find common solutions.

Tags

CCSS.HSA.REI.C.7

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented by a straight line on a graph.

Front

What is the graphical representation of a quadratic equation?

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A quadratic equation is represented by a parabola on a graph.

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CCSS.HSF-IF.C.7A

Front

How can you determine the number of solutions in a linear-quadratic system?

Back

The number of solutions can be determined by analyzing the intersection points of the linear and quadratic graphs.

Tags

CCSS.HSA.REI.C.7

Front

What does it mean if a system has no solutions?

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A system has no solutions if the graphs of the equations do not intersect, indicating that there are no common points.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system has one solution?

Back

A system has one solution if the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system has two solutions?

Back

A system has two solutions if the graphs of the equations intersect at two distinct points.

Tags

CCSS.8.EE.C.8B

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 its orientation.

Front

How do you find the vertex of a quadratic equation in standard form?

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The vertex can be found using the formula (-b/2a, f(-b/2a)) for a quadratic equation in the form ax^2 + bx + c.