To determine the correct statement about the parabola, let's analyze each option:
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The vertex and the x-intercepts share the same point.
- This statement would be true if the vertex were located on the x-axis (i.e., the point where the parabola touches or crosses the x-axis). However, typically, a parabola can have a vertex that is not at an x-intercept unless it's specifically designed that way (like a parabola that touches the x-axis).
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The y-intercept and the vertex share the same point.
- This statement would only be true if the vertex itself lies on the y-axis. Generally, the vertex and y-intercept do not coincide unless the parabola is symmetric around the y-axis and the vertex happens to be at the origin.
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The y-intercept and the x-intercepts share the same point.
- This can only occur if the parabola passes through the same point at both the y-axis (where it intersects) and at a point on the x-axis. This is typically not the case since one intercept is vertical and the other is horizontal.
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There is only one x-intercept.
- This is only true for parabolas that are either tangent to the x-axis or that open up/down without crossing the x-axis more than once.
Without the visual of the parabola to analyze its vertex, intercepts, and shape, we can logically conclude from general properties of parabolas that if it appears to touch the x-axis, it could likely have a single x-intercept while being above or below the x-axis otherwise.
Therefore, given the context of your question, the most plausible answer would be "There is only one x-intercept."
If you have access to the visual information, verifying these statements through the graph would provide a more precise conclusion.
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