Quadratic Linear Systems

Front

What is a quadratic linear system?

Back

A system of equations that includes at least one quadratic equation and one linear equation.

Front

What is the general form of a quadratic equation?

Back

The general form is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are constants.

Front

How many solutions can a quadratic linear system have?

Back

A quadratic linear system can have 0, 1, or 2 solutions.

Front

What does it mean if a quadratic linear system has no solutions?

Back

It means the graphs of the equations do not intersect.

Front

What does it mean if a quadratic linear system has one solution?

Back

It means the graphs of the equations touch at one point (tangent).

Front

What does it mean if a quadratic linear system has two solutions?

Back

It means the graphs of the equations intersect at two distinct points.

Front

How do you find the solutions to a quadratic linear system graphically?

Back

By plotting both equations on the same graph and identifying the points of intersection.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.