Please help me out.........
2 answers:
Answer:
vertex = (- 3, 24)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0, then
The x- coordinate of the vertex is
= -
y = - x² - 6x + 15 ← is in standard form
with a = - 1, b = - 6, thus
= -
= - 3
Substitute x = - 3 into the function for corresponding value of y
y = - (- 3)² - 6(- 3) + 15 = - 9 + 18 + 15 = 24
vertex = (- 3, 24)
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Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.
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This means that the confidence interval is
The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85
To find the confidence interval, we first find the z-score associated with it:
Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.
We calculate the margin of error using
This means that the confidence interval is
The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85