Solving Linear/Quadratic Systems by Graphing

Front

What is a linear system?

Back

A linear system consists of two or more linear equations that share the same variables.

Front

What is a quadratic system?

Back

A quadratic system includes at least one quadratic equation and one linear equation.

Front

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

Back

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

Front

What does it mean if a system has no solution?

Back

It means the lines (or curves) do not intersect; they are parallel or do not meet.

Front

What does it mean if a system has one solution?

Back

It means the lines (or curves) intersect at exactly one point.

Front

What does it mean if a system has two solutions?

Back

It means the graphs intersect at two distinct points.

Front

What is the vertex of a parabola?

Back

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

Front

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

Back

By analyzing the intersection points of the linear and quadratic graphs.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The discriminant (b² - 4ac) determines the number of real solutions: positive (2 solutions), zero (1 solution), negative (no real solutions).