To determine which statement about the parabola is true, we need to analyze the characteristics of a parabola based on its shape and key points such as the vertex, x-intercepts, and y-intercept.
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The y-intercept and the x-intercepts share the same point.
- This is only true if the value that the parabola crosses the y-axis is also one of the x-intercept points. This is generally not true for most parabolas unless they have specific symmetry and location.
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The vertex and the x-intercepts share the same point.
- This statement is only true if the vertex of the parabola lies exactly on the x-axis where it crosses. This typically only occurs in parabolas that are tangent to the x-axis.
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There is only one x-intercept.
- A parabola can have either two x-intercepts, one (if it just touches the x-axis), or none (if it opens above the x-axis). This statement might be true if the parabola is tangent to the x-axis.
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The y-intercept and the vertex share the same point.
- This is only true in specific parabolas where the vertex is positioned directly on the y-axis. It’s not generally true for all parabolas.
Without seeing the specific image of the parabola, determining the truth of the statements is difficult. However, if the parabola only touches the x-axis at its vertex, then the statement "There is only one x-intercept" would be true.
If the parabola clearly has distinct x-intercepts and a y-intercept that is separate from the vertex, the first three statements likely wouldn't hold.
Based on typical options given the nature of most parabolas, the most likely correct statement is "There is only one x-intercept," assuming the parabola is tangent to the x-axis.
Please check the specific graph to confirm which one fits.