What point is symmetrical to (−1,−17) for the graph of y=−x2−16 ?(1 point) Responses (−17,−1) left parenthesis negative 17 comma negative 1 right parenthesis (1,17) left parenthesis 1 comma 17 right parenthesis (−1,17) left parenthesis negative 1 comma 17 right parenthesis (1,−17)
To find the point that is symmetrical to the point (-1, -17), we need to find the corresponding point that has the same distance from the axis of symmetry.
The equation y = -x^2 - 16 represents a parabola that opens downwards and has its vertex at the point (0, -16).
The axis of symmetry is a vertical line passing through the vertex, which in this case is the line x = 0 (the y-axis).
Since the point (-1, -17) is one unit to the left of the axis of symmetry, the corresponding point that is one unit to the right of the axis of symmetry would be (1, -17).
Therefore, the point that is symmetrical to (-1, -17) for the graph of y = -x^2 - 16 is (1, -17).
To find the point that is symmetrical to (-1,-17) for the graph of y = -x^2 -16, we can apply the principle of symmetry.
The equation y = -x^2 -16 represents a downward facing parabola with its vertex at (0, -16). The line of symmetry is the vertical line passing through the vertex.
Since the point (-1,-17) is one unit to the left of the vertex, the symmetrical point will be one unit to the right of the vertex.
Therefore, the symmetrical point to (-1,-17) is (1,-17).
To find the point that is symmetrical to (-1, -17) for the graph of y = -x^2 - 16, you need to reflect the given point across the line of symmetry.
In this case, the line of symmetry is the y-axis because the equation is in the form y = f(x) (a symmetrical function). So, all points on the graph that have the same x-values but opposite y-values are symmetrical to each other.
To reflect a point across the y-axis, you need to change the sign of the y-coordinate. Therefore, the symmetrical point to (-1, -17) will have the same x-coordinate (-1) but the y-coordinate will be positive. So, the correct answer is (−1, 17).