What parent function describes the set (-1, -1), (0, 0), (1, -1) (-2, -8), (2, -8)?
So should I write f(x) = x^2 or f(x) = -x^2 for the parent function?
To determine the parent function that describes the set of points (-1, -1), (0, 0), (1, -1), (-2, -8), (2, -8), let's analyze the given points.
We notice that for x values -1, 0, and 1, the corresponding y values are -1, 0, and -1. This suggests the presence of symmetry in the graph.
To identify the type of symmetry, we need to compare the y values. Since (-1, -1) and (1, -1) have the same y values, the graph exhibits symmetry with respect to the y-axis.
Additionally, for x values -2 and 2, the y values are -8, indicating that the graph is symmetric with respect to the x-axis.
Considering both the symmetries, we can conclude that the parent function for this set of points is a quadratic function with both x-axis and y-axis symmetries.
Since a quadratic function can have either an upward or downward opening, we need to determine the direction of the opening.
Comparing the given points, (-1, -1), (0, 0), and (1, -1), we can see that the shape of the graph is concave downward because the highest point, (0, 0), is located between the other two points.
Therefore, the parent function that describes this set of points is f(x) = -x^2.
In summary, you should write f(x) = -x^2 for the parent function that matches the given set of points.