Solving Quadratic Linear Systems

Front

What is a quadratic linear system?

Back

A quadratic linear system consists of a quadratic equation (a polynomial of degree 2) and a linear equation (a polynomial of degree 1) that are solved simultaneously.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations. If both equations are satisfied, the point is a solution.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations do not intersect, indicating that there are no common points.

Front

What does it mean if a system of equations has one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean if a system of equations has two solutions?

Back

It means that the quadratic equation intersects the linear equation at two distinct points.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

How can you find the vertex of a quadratic equation in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.