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.

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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.

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.

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.

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.

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.

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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.

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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?

Back

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).

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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.