Answer:
- quadratic polynomial
- minimum at (1, -9)
- decreasing on (-1, 1)
Step-by-step explanation:
1. First differences in the y-values are ...
... -5-0 = -5; -8-(-5) = -3; -9-(-8) = -1; -8-(-9) = 1; -5-(-8) = 3; 0-(-5) = 5
Second differences are ...
... -3-(-5) = 2; -1-(-3) = 2; 1-(-1) = 2; 3-1 = 2; 5-3 = 2
These 2nd differences are constant, so the points can be described by a 2nd-degree polynomial.
2. Values on the graph range from 0 to a low of -9 and back up to 0. There is a minimum at (1, -9).
3. The value at x=-1 is -5; at x=1, it is -9, which is less than -5. The function is decreasing on the interval -1 to 1.
