Solving Systems of linear and quadratic equations

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What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is a system of quadratic equations?

Back

A set of two or more quadratic equations that can be solved simultaneously. Solutions are the points where the graphs intersect.

Tags

CCSS.HSA.REI.C.7

Front

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

Back

Plot both equations on the same graph and identify the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the elimination method for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is a quadratic function?

Back

A function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the discriminant in a quadratic equation?

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The value calculated as b² - 4ac, which determines the nature of the roots: positive (two real roots), zero (one real root), or negative (no real roots).

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a system to have infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A