6.1 Quadratic Linear Systems

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

It means that the graphs of the equations do not intersect at any point.

By analyzing the graphs of the equations or using algebraic methods to find intersection points.

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

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

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

The discriminant (b^2 - 4ac) determines the number of real solutions: if >0, two solutions; =0, one solution; <0, no solutions.

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

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

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.