The functions f(x) = (x + 1)2 − 2 and g(x) = −(x − 2)2 + 1 have been rewritten using the completing-the-square method. Is the ve
rtex for each function a minimum or a maximum? Explain your reasoning for each function.
1 answer:
Answer:
- f(x) vertex is a minimum
- g(x) vertex is a maximum
Step-by-step explanation:
The reasoning is the same in each case: the sign of the coefficient of the squared term indicates the direction the parabola opens. If it opens upward, the vertex is a minimum; if it opens downward, the vertex is a maximum.
f(x) -- the sign of the squared term is positive, so the vertex is a <em>minimum</em>.
g(x) -- the sign of the squared term is negative, so the vertex is a <em>maximum</em>.
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The sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
p-hat proportion:
In this proportion, "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.
The general form for calculating p-hat proportion is,
where
x is the number of successes in the sample, and
y is the size of the sample.
Given,
In a random sample of 200 engineers, 137 have a master's degree.
Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees
According to the question,
x = 137 (number of successes in the sample)
and y = 200 (size of the sample)
Now apply the value on the formula then we get,
So, the value of p-hat is
The results are usually reported as a percentage, which in this case would be
=> 0.685 x 100 = 68.5%
Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
To know more about p-hat proportion here
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