Answer:
True
Step-by-step explanation:
For any function of the form the coefficient a produces a reflection of the function whenever
.
We can verify it in the following way.
Take, for example, the function:
Now let's make
Now let's in the following function:
We have:
We can see then that the function was reflected in the axis -y by placing a negative coefficient a.
You can see more examples in the attached images
Therefore we can conclude that the statement is true.
Using the recurrence relation, we can find a couple more values in the sequence:
First differences are 0, 2, 4, 6, ...
Second differences are constant at 2, so the function is quadratic.
The sequence can be described by the quadratic ...
... an = n² -n +2
_____
We know the value for n=0 is 2, so we can find <em>a</em> and <em>b</em> using the given values for a1 and a2.
... an = an² +bn +2
... a1 = 2 = a·1² +b·1 +2 . . . . for n=1
... a + b = 0
... a2 = 4 = a·2² -a·2 +2 . . . . for n = 2; using b=-a from the previous equation
... 2 = 2a
... a = 1 . . . . so b = -1
