Quadratic Linear Systems

Front

What is a quadratic linear 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 does it mean if a system has 0 solutions?

Back

The graphs of the equations do not intersect.

Front

What does it mean if a system has 1 solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean if a system has 2 solutions?

Back

The graphs of the equations intersect at two distinct points.

Front

What is the general form of a quadratic equation?

Back

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

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point on the graph of the quadratic function.

Front

How can you find the solutions of a quadratic equation graphically?

Back

By identifying the x-coordinates of the points where the graph intersects the x-axis.

Front

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

Back

It determines the number of real solutions: if positive, 2 solutions; if zero, 1 solution; if negative, 0 solutions.

Front

What is the standard form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.