Question

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 O comma 5 right parenthesis.
Determine which of the following statements is true about the parabola.
(1 point)
• The y-intercept and the x-intercepts share the same point.
• The vertex and the x-intercepts share the same point.
• There is only one x-intercept.
• The y-intercept and the vertex share the same point.

Answer 1

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 is (0,5), which is the vertex; there are no real x-intercepts.