Algebra 2: Systems of Equations (Linear and Quadratic)

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a quadratic equation?

Back

A parabola, which can open upwards or downwards depending on the coefficient of the x^2 term.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How do you find the intersection of a linear and a quadratic equation?

Back

Set the equations equal to each other and solve for the variable.

Front

What is the vertex of a parabola?

Back

The highest or lowest point on the graph of a quadratic function.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The value calculated as b^2 - 4ac, which determines the number of real solutions.

Front

What does a positive discriminant indicate?

Back

Two distinct real solutions for the quadratic equation.