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Use the image to answer the question.

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

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

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

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

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

1 answer

Without being able to see the image of the parabola, we can still analyze the statements based on general properties of parabolas:

  1. There is only one x-intercept.
    This statement would only be true if the parabola touches the x-axis at exactly one point (a double root), which occurs at the vertex.

  2. The y-intercept and the vertex share the same point.
    This can only be true if the vertex of the parabola is located on the y-axis.

  3. The vertex and the x-intercepts share the same point.
    This statement would imply that the vertex of the parabola is also one of the x-intercepts, which can occur if the vertex is on the x-axis (again, at the point of a double root).

  4. The y-intercept and the x-intercepts share the same point.
    This is generally not true for standard parabolas, as the y-intercept is when x=0, while x-intercepts depend on the roots of the equation.

Given the nature of parabolas, if the vertex is the only point on the x-axis (the parabola touches the x-axis at its vertex), the correct option would be likely the first statement: "There is only one x-intercept."

However, without the actual image, this is only a reasoned assumption. You should refer back to the graph to identify the correctness of these properties directly; the image will be crucial in determining which statement is true.