Can someone help me some this
2 answers:
Answer:
Step-by-step explanation:
vertex form of parabola: y = a(x - h)² + k
where (h, k) is the vertex
Given vertex = (4, -2) :
⇒ y = a(x - 4)² - 2
Given y-intercept = (0, 6) substitute values into equation and solve for a:
⇒ 6 = a(0 - 4)² - 2
⇒ 6 = 16a - 2
⇒ 16a = 8
⇒ a = 1/2
Therefore, equation of parabola:
⇒ y = 1/2(x - 4)² - 2
⇒ y = 1/2(x² - 8x + 16) - 2
⇒ y = (1/2)x² - 4x + 6
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Answer:
One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:
Iaₙ₊₁I < IaₙI
This means that the absolute value of the terms must decrease as n increases.
Then we must have:
We can write this as:
If we assume that n is a really big number, then:
n + 1 ≈ 1
And we can write:
Then we have the inequality
And remember that this must be in absolute value, then we will have that:
-1 < (x - 2)/3 < 1
-3 < x - 2 < 3
-3 + 2 < x < 3 + 2
-1 < x < 5
The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.