6.1 Quadratic Linear Systems

Front

What is a quadratic-linear system?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

What is the general form of a quadratic equation?

Back

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

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

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

Front

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

Back

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

Front

What does it mean for a system to have two solutions?

Back

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

Front

How can you solve a quadratic-linear system graphically?

Back

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

Front

What is the y-intercept of a linear equation?

Back

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