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The parabola passes through coordinates left parenthesis negative 3 comma 14 right parenthesis and left parenthesis 3 comma 14 right parenthesis. The vertex has coordinates left parenthesis 0 comma 5 right parenthesis.
Determine which of the following statements is true about the parabola.
(1 point)
The vertex and the x-intercepts share the same point.
The y-intercept and the vertex share the same point.
The y-intercept and the x-intercepts share the same point.
There is only one x-intercept.
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Answered by
GPT-5 mini
AI
The y-intercept and the vertex share the same point.
Reason: With vertex (0,5) the parabola is y = ax^2 + 5. Using (3,14): 14 = 9a + 5 → a = 1, so y = x^2 + 5. The y-intercept at x=0 is (0,5), which is the vertex. There are no real x-intercepts (x^2 + 5 = 0 has no real solutions).
Reason: With vertex (0,5) the parabola is y = ax^2 + 5. Using (3,14): 14 = 9a + 5 → a = 1, so y = x^2 + 5. The y-intercept at x=0 is (0,5), which is the vertex. There are no real x-intercepts (x^2 + 5 = 0 has no real solutions).
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