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A parabola is graphed on a coordinate plane. The x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 1 to 16 in increments of 1.

Determine which of the following statements is true about the parabola.

(1 point)
Responses

The y-intercept and the vertex share the same point.
The y -intercept and the vertex share the same point.

There is only one x-intercept.
There is only one x -intercept.

The y-intercept and the x-intercepts share the same point.
The y -intercept and the x -intercepts share the same point.

The vertex and the x-intercepts share the same point.

1 answer

To determine which statement is true about the parabola based on its graph, let's analyze each option:

  1. The y-intercept and the vertex share the same point.
    This would mean that the parabola touches the y-axis at its vertex. This is generally not the case unless the vertex lies on the y-axis, which is not typical for most parabolas.

  2. There is only one x-intercept.
    A parabola can have zero, one, or two x-intercepts depending on its position relative to the x-axis. If the parabola is tangent to the x-axis, then it will have one x-intercept, but this must be confirmed by examining the graph.

  3. The y-intercept and the x-intercepts share the same point.
    This statement suggests that the point where the parabola crosses the y-axis (the y-intercept) is also an x-intercept. This is only possible if the parabola crosses the y-axis at the same point it touches the x-axis, which is generally not the case.

  4. The vertex and the x-intercepts share the same point.
    If the vertex of the parabola is also an x-intercept, it means the parabola is at its lowest or highest point (depending on the direction it opens) right on the x-axis. This can happen if its vertex lies at an x-intercept.

To determine the correct response, you would need to examine the graph of the parabola to see how many x-intercepts it has, where the vertex is located, and where the y-intercept is.

Assuming you observe only one x-intercept on the graph, and that the vertex is at that same x-intercept, then you would select “The vertex and the x-intercepts share the same point.”

If the details were clearer regarding the position of the y-intercept relative to the others, one could make a more informed choice. Without seeing the graph, it is not possible to definitively select the correct answer, but "There is only one x-intercept" or "The vertex and the x-intercepts share the same point" could be valid depending on the specific graph.

Please refer to the graph to see how many x-intercepts there are and the locations of the y-intercept and vertex to select the true statement.