To determine where the parabola intersects the x-axis, we need to analyze the given information:
- The vertex of the parabola is at the point \( (1, -7) \).
- The parabola intersects the x-axis between \( x = 6 \) and \( x = 7 \).
Since the vertex is at \( (1, -7) \) and the parabola intersects the x-axis to the right of the vertex (at points greater than 1), we can infer that the parabola opens upwards.
Given that the parabola opens upwards, it will also intersect the x-axis on the left side of the vertex. Since we know that it intersects the x-axis between \( 6 \) and \( 7 \) on the right, it can be concluded that it will also likely intersect the x-axis in the negative region.
A parabola that opens upwards and has its vertex at a point in the third quadrant (where \( x < 1 \) and \( y < 0 \)) will cross the x-axis twice, once on the left side of the vertex and once on the right.
To estimate where the parabola might intersect the x-axis on the left side, we can gather clues from symmetry. The linear distance between the vertex and the intersections of the x-axis on the right side gives us some information for the left side as well.
Since we know it intersects the x-axis between \( 6 \) and \( 7 \):
- The distance from the vertex over to the right (6 to 7) is approximately \( 6 - 1 = 5 \) units.
Using symmetry, we can expect that the distance to the left might also be about \( 5 \) units. Therefore:
- On the left, we could estimate about \( 1 - 5 = -4 \).
This suggests that the parabola will intersect the x-axis in a negative integer between \( -5 \) and \( -4 \).
Thus, the answer is: D. between negative 5 and negative 4.