Quadratic Linear Systems

Front

What is a linear-quadratic system?

Back

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

Front

How many solutions can a linear-quadratic system have?

Back

0, 1, or 2 solutions.

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 quadratic function?

Back

The highest or lowest point of the parabola, found at the coordinates (h, k) in the vertex form y = a(x-h)^2 + k.

Front

What does it mean for a system to have no solutions?

Back

The graphs of the equations do not intersect; they are parallel.

Front

What is the discriminant in a quadratic equation?

Back

The value calculated as b^2 - 4ac, which determines the number of real solutions.

Front

What does a positive discriminant indicate?

Back

There are two distinct real solutions to the quadratic equation.

Front

What does a zero discriminant indicate?

Back

There is exactly one real solution (the vertex touches the x-axis).

Front

What does a negative discriminant indicate?

Back

There are no real solutions (the parabola does not intersect the x-axis).

Front

How can you find the intersection points of a linear and a quadratic function?

Back

Set the equations equal to each other and solve for x.