Question

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

(1 point)
Responses

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

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.

Answer 1

I don’t have the equation or graph of the specific parabola you mean, so I can’t pick which single statement is true for that parabola. None of the four statements is true for every parabola — each can be true for some parabolas and false for others. Examples:

- "The y‑intercept and the x‑intercepts share the same point." — true for y = x^2 (all are (0,0)); false for y = x^2 − 1 (y‑intercept (0,−1), x‑intercepts (±1,0)).
- "There is only one x‑intercept." — true for y = (x−1)^2 (single x‑intercept at (1,0)); false for y = x^2 − 1 (two x‑intercepts).
- "The y‑intercept and the vertex share the same point." — true for y = x^2 (vertex and y‑intercept both (0,0)); false for y = (x−1)^2 + 1 (vertex (1,1), y‑intercept (0,2)).
- "The vertex and the x‑intercepts share the same point." — true for y = (x−1)^2 (vertex (1,0) is an x‑intercept); false for y = x^2 − 1 (vertex (0,−1) is not an x‑intercept).

If you post the parabola’s equation or its graph, I’ll identify which of the four statements is true for that specific parabola.