Quadratic Linear system

Front

What is a quadratic-linear system?

Back

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

Front

How many solutions can a quadratic-linear system have?

Back

It could have no solutions, one solution, or infinite solutions.

Front

What does it mean if a quadratic equation has two zeros?

Back

It means the parabola intersects the x-axis at two points.

Front

What is the maximum number of solutions for a linear system?

Back

A linear system can have either one solution, no solutions, or infinitely many solutions.

Front

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

Back

By analyzing the intersection points of the graphs of the equations.

Front

What is the solution to the system: x - 3y = 8 and x + 3y = 2?

Back

(5, -1)

Front

What does the vertex of a parabola represent?

Back

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

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: if positive, two solutions; if zero, one solution; if negative, no real solutions.

Front

How can you graph a quadratic function?

Back

By plotting the vertex, axis of symmetry, and additional points, then drawing a smooth curve.