Use the parabola tool to graph the quadratic function f(x)=(x-5)^2+1
1 answer:
Answer:
Look to the attached graph
Step-by-step explanation:
* Lets revise how to graph the quadratic function
- Find the vertex of it
- Find the y-intercept
- Find the x-intercept
∵ f(x) = (x - 5)² + 1 ⇒ the completing square form
- The completing square form for any quadratic is
( x - h)² + k, where h and k are the coordinate of the vertex point
* Lets compare the two forms
∵ (x - h)² + k = (x - 5)² + 1
∴ h = 5 and k = 1
∴ The vertex of the parabola is (5 , 1)
- To find the x-intercept put f(x) = 0
∵ (x - 5)² + 1 = 0 ⇒ subtract 1 from both sides
∴ (x - 5)² = -1 ⇒ the square can not give -ve number
∴ The parabola does not intersect the x-axis
- To find the y-intercept put x = 0
∵ f(0) = (0 - 5)² + 1 = 25 + 1 = 26
∴ The parabola intersects the y-axis at point (0 , 26)
- The parabola is opened upward because the coefficient of x² is +ve
* Now lets graph it
- Look to the attached graph
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Answer:
The corresponding point estimate is 0.882.
The sample standard deviation is 1.373.
Step-by-step explanation:
The data set is:
S = {25.01, 25.87, 26.34, 26.51, 26.75, 27.24, 27.40, 27.63, 27.83, 27.90, 28.08, 28.13, 28.37, 28.58, 28.59, 28.96, 29.20, 29.22, 29.38, 30.88}
Compute the mean as follows:
Subtract the mean from each value and take the modulus of those values.
The new data set is:
S₁ = {2.8835, 2.0235, 1.5535, 1.3835, 1.1435, 0.6535, 0.4935, 0.2635, 0.0635, 0.0065, 0.1865, 0.2365, 0.4765, 0.6865, 0.6965, 1.0665, 1.3065, 1.3265, 1.4865, 2.9865}
Arrange these values in ascending order as follows:
S₂ = {0.0065 , 0.0635 , 0.1865 , 0.2365 , 0.2635 , 0.4765 , 0.4935 , 0.6535 , 0.6865 , 0.6965 , 1.0665 , 1.1435 , 1.3065 , 1.3265 , 1.3835 , 1.4865 , 1.5535 , 2.0235 , 2.8835 , 2.9865}
There are 20 observations in the data set.
The median value for an even set of values is the mean of the middle two values.
In this case the median will be the mean of the 10th and 11th observations.
Thus, the corresponding point estimate is 0.882.
Compute the standard deviation as follows:
In set S₁ we computed the absolute mean deviations.
Now take the square of these values and divide by (n - 1) to compute the sample variance:
Compute the sample standard deviation as follows:
Thus, the sample standard deviation is 1.373.