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 0 comma 5 right parenthesis.


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

Answer 1

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

Reason: Symmetry about x=0 with vertex (0,5) gives 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 since x^2 + 5 = 0 has no real solutions.