To determine the correct statement about the given points on the parabola, we need to identify which points are high points (maximum) and which are low points (minimum).
The points provided are:
- (-1, -1)
- (-0.75, 2.375)
- (-0.5, 5)
- (-0.25, 8)
- (0.25, 8.375)
- (0.5, 0.75)
- (1, 5)
From these points, we can analyze their corresponding y-values:
- For x = -1, y = -1
- For x = -0.75, y = 2.375
- For x = -0.5, y = 5
- For x = -0.25, y = 8
- For x = 0.25, y = 8.375 (this is the highest value)
- For x = 0.5, y = 0.75
- For x = 1, y = 5
The highest point among these y-values is at (0.25, 8.375). This point can be considered the "high point" or maximum of the parabola.
The lowest y-value is at (-1, -1), which would be the "low point" or minimum of the parabola.
Based on the options given:
- (0.5, 9) is not a point from the data.
- (0.25, 8.375) is indeed the high point on the parabola.
- (0.25, 8.375) as a low point is incorrect.
- (−1, −1) is the low point, which is also correct.
Thus, the correct statements are:
- (0.25, 8.375) is the high point on the parabola.
- (−1,−1) is the low point on the parabola.
If you need to select only one correct response, (0.25, 8.375) is the high point on the parabola would be the best choice.