Answer:
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Hi. I was unsure of what exactly you wanted from this equation, so here's a quick analysis:
<em>f(x) = 2(x - 3)^2 - 2</em>
<em></em>
Domain: (-∞, ∞)
Range: (-2, ∞)
X-intercepts: (4, 0), (2, 0)
Y-intercept: (0, 16)
Axis of Symmetry: x = 3
Minimum value (vertex): (3, -2)
Standard form: y = 2x^2 - 12x + 16
The question as presented is incomplete, here is the complete question with the multiple choice:
The sequence a1 = 6, an = 3an − 1 can also be
written as:
1) an = 6 ⋅ 3^n
2) an = 6 ⋅ 3^(n + 1)
3) an = 2 ⋅ 3^n
4) an = 2 ⋅ 3^(n + 1)
The correct choice is option 3) an = 2⋅3^n.
If we look at the initial sequence an = 3⋅an-1, and
a1 = 3⋅a0 = 6
a0 = 6/3
a0 = 2
We can now look at the sequence.
a0 = 2
a1 = 6
a2 = 18
a3 = 54
etc...
A common factor in each of those numbers is 2, so we can rewrite the sequence by factoring out 2.
a0 = 2⋅1
a1 = 2⋅3
a2 = 2⋅9
a3 = 2⋅27
The numbers being multiplied by 2 are all factors of 3. So we can rewrite the sequence again as:
a0 = 2⋅3^0
a1 = 2⋅3^1
a2 = 2⋅3^2
a3 = 2⋅3^3
This sequence can now be rewritten as an = 2⋅3^n.
For number 2. The pilot flew 4 circuits and in total by the 5th day he flew 14 right?
