To determine which statement about the parabola is true, we need to consider the definitions of the terms used:
- Y-intercept: The point where the parabola intersects the y-axis. It has the form (0, y).
- Vertex: The highest or lowest point of the parabola, depending on its direction (opening upwards or downwards).
- X-intercepts: The points where the parabola intersects the x-axis. These points have the form (x, 0).
Now let's evaluate the statements:
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The y-intercept and the vertex share the same point. - This is not generally true for all parabolas. It could be true for some specific cases, but not a general characteristic.
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The vertex and the x-intercepts share the same point. - This is also not true in general. While the vertex can lie on the same x-coordinate as one or both x-intercepts in specific cases, it doesn't generally hold for all parabolas.
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The y-intercept and the x-intercepts share the same point. - This is not typically the case as well. The y-intercept occurs at (0, y), while x-intercepts occur at points where y = 0.
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There is only one x-intercept. - This is true if the parabola touches the x-axis but does not cross it, meaning it has a double root. If the discriminant of the quadratic equation is zero, there will be one x-intercept.
Without seeing the actual graph, the statement "There is only one x-intercept" is often the most likely true statement in cases where the parabola touches the x-axis but does not cross it. Thus, if the graph features such behavior, this would be the correct answer.
If there is confirmation from the image that matches this scenario, you would choose "There is only one x-intercept." If you see that the parabola indeed has two x-intercepts or none, you would adjust accordingly.
2 answers