Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).
1 answer:
Answer:
f(x) = 9(x -1/3)^2 -3
Step-by-step explanation:
In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...
y = a(x -h)^2 +k
To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":
1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given
1 = (4/9)a -3 . . . . simplify
4 = (4/9)a . . . . . . add 3
9 = a . . . . . . . . . . multiply by 9/4
The quadratic function you desire is ...
f(x) = 9(x -1/3)^2 -3
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Answer:
And the 99% confidence interval would be given (0.647;0.753).
So the correct answer would be:
a. 0.647 and 0.753
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
The estimated population proportion for this case is:
The confidence interval would be given by this formula
For the 99% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 99% confidence interval would be given (0.647;0.753).
So the correct answer would be:
a. 0.647 and 0.753