Been stuck on this for a while man....................
2 answers:
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Answer:
True.
Step-by-step explanation:
The explicit form for an arithmetic sequence is:
where is the first term and
is the common difference.
The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.
Yes, the common difference is the slope.
So we have d=2.
The first term is 9.5 because that is what happens when x=1.
x is n.
y is .
So the answer is true.
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You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:
Let n=1:
Let n=2:
Let n=3:
Let n=4:
Let n=5:
Let n=6:
We have confirmed that we get all 6 of the mentioned points using the equation they gave.
Write the vertex form of the equation and find the necessary coefficient to make it work.
.. y = a*(x +3)^2 -2
.. = ax^2 +6ax +9a -2
You require the y-intercept to be 7. So, for x=0, you have
.. 9a -2 = 7
.. 9a = 9
.. a = 1
The equation you seek is
.. y = x^2 +6x +7
.. y = a*(x +3)^2 -2
.. = ax^2 +6ax +9a -2
You require the y-intercept to be 7. So, for x=0, you have
.. 9a -2 = 7
.. 9a = 9
.. a = 1
The equation you seek is
.. y = x^2 +6x +7