Which of the following descriptions accurately characterizes a graph that has no real roots? (1 point)
a graph that only touches the x-axis, but does not cross it
a graph that touches the x-axis twice
a graph that does not touch the x-axis
a graph that overlaps the x-axis
a graph that does not touch the x-axis
A graph that does not touch the x-axis accurately characterizes a graph that has no real roots.
To determine which of the given descriptions accurately characterizes a graph with no real roots, you need to understand what it means for a graph to have real roots. The roots of a graph represent the x-values at which the graph intersects or crosses the x-axis.
If a graph has no real roots, it means there are no x-values for which the graph intersects or crosses the x-axis. In other words, the graph never touches or crosses the x-axis.
Based on this understanding, the correct description that characterizes a graph with no real roots is:
A graph that does not touch the x-axis.
This accurately represents the absence of any x-values for which the graph intersects or crosses the x-axis.