Solving Linear and Quadratic Systems by Graphing

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

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

Back

By finding the points of intersection between the linear and quadratic graphs; the number of intersection points indicates the number of solutions.

Front

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

Back

It means the graphs do not intersect, indicating that the equations represent parallel lines and a parabola that does not touch the line.

Front

What does it mean if a linear-quadratic system has one solution?

Back

It means the graphs intersect at exactly one point, indicating that the line is tangent to the parabola.

Front

What does it mean if a linear-quadratic system has two solutions?

Back

It means the graphs intersect at two distinct points, indicating that the line crosses the parabola at two locations.

Front

How do you graph a linear equation?

Back

Identify the y-intercept and use the slope to find another point; then draw a straight line through these points.

Front

How do you graph a quadratic equation?

Back

Identify the vertex, axis of symmetry, and plot additional points; then draw a smooth curve through these points.

Front

What is the vertex of a parabola?

Back

The highest or lowest point of the parabola, depending on its orientation (opening upwards or downwards).

Front

What is the axis of symmetry in a quadratic function?

Back

A vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).