To determine the truth of these statements about a parabola, let's briefly analyze what each term typically means:
- Vertex: The highest or lowest point on the parabola, depending on its orientation (opening up or down).
- Y-intercept: The point where the parabola crosses the y-axis (x = 0).
- X-intercepts: The points where the parabola crosses the x-axis (y = 0).
Now let's evaluate the statements:
-
The y-intercept and the vertex share the same point.
This is generally not true for most parabolas, as the vertex can be at a different y-value compared to the y-intercept. -
The vertex and the x-intercepts share the same point.
This statement is not typically true; for most parabolas, the vertex will not be on the x-axis unless it is a special case (a parabola that opens up or down and is tangent to the x-axis). -
The y-intercept and the x-intercepts share the same point.
This can only be true if the parabola passes through the origin (0,0), which is also a specific case. -
There is only one x-intercept.
This could be true if the parabola opens up or down and is tangent to the x-axis (making the vertex the only x-intercept).
Without seeing the specific parabola, the most universally applicable and likely true statement about many parabolas is:
There is only one x-intercept.
Because while the other statements can only be true in specific configurations, there are many parabolas (especially those that open up or down) that can have only one x-intercept if the vertex is located on the x-axis.
In conclusion, without additional details about the specific parabola's vertex and intercepts, the most plausible true statement is:
There is only one x-intercept.