What point is symmetrical to (−1,−17) for the graph of y=−x2−16?(1 point)

Question

Responses

(−17,−1)
left parenthesis negative 17 comma negative 1 right parenthesis

(−1,17)
left parenthesis negative 1 comma 17 right parenthesis

(1,−17)
left parenthesis 1 comma negative 17 right parenthesis

(1,17)

Answer 1

To find the point symmetrical to \((-1, -17)\) with respect to the graph of the function \(y = -x^2 - 16\), we need to identify the reflection with respect to the axis of symmetry of the parabola.

The function \(y = -x^2 - 16\) is a downward-opening parabola with its vertex at the point \((0, -16)\). The axis of symmetry is the vertical line \(x = 0\).

To find the symmetrical point of \((-1, -17)\), we can reflect it across the axis of symmetry. The \(x\)-coordinate of the point will change sign, while the \(y\)-coordinate remains the same.

1. The \(x\)-coordinate of the original point \((-1, -17)\) is \(-1\). Reflecting across \(x = 0\) gives us \(1\).
2. The \(y\)-coordinate remains \(-17\).

Thus, the symmetrical point is \((1, -17)\).

So the correct response is:

\((1, -17)\)