Explain how the location of the vertex and the direction of the opening (upwards or downwards) affects the domain and range of the quadratic function. Use complete sentences.

Answer 1

The location of the vertex and the direction of the opening affect the range of the quadratic function. If the direction of the opening is up, then the lowest y-value possible is the y-coordinate of the vertex (v) and all y-values above it are included in the range. In other words, the range is y ≥ v. If it opens down, however, then the y-coordinate of the vertex is the highest y-value possible and all y-values below it are included in the range. So in that case, y ≤ v.

The domain of a quadratic function is not affected by either of these, as it will continue both to the left and to the right indefinitely, from negative infinity to positive infinity.