Mathematics, 04.01.2020 08:31, zoseta

Anew hospital tracked the number of births during its first 6 months of operation, as shown in the table. find a quadratic function that models the data. round numerical values to the nearest whole number. f(x) = x2 + x + use the function to predict the number of births for month 8. there will be about births..

Anew hospital tracked the number of births during its first 6 months of operation, as shown in the t

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answered: keniaguevara32

Let    x refers to the Month numbers
And y refers to Number of births

There is 5 steps to find the quadratic function that models the data.

First step           ⇒ Plot the data pairs (x, y) in a coordinate plane.
                              which are the blue circles in the attached figure

Second step     ⇒ Draw the parabola you think best fits the data.
                             Which is the red function in the attached figure.

Third step       ⇒ Estimate the coordinates of three points on the
                             parabola, which are (2, 108), (4, 68), and (6, 75).
                             which are the black squares in the attached figure

Fourth step       ⇒ Substitute the coordinates of the points into the model
                            y = ax2 + bx + c
                            to obtain a system of three linear equations.

                            4a + 2 b + c = 108   ---------(1)
                        16a + 4 b + c = 68   ---------(2)
36a + 6 b + c = 75 ---------(3)

Fifth step   ⇒ Solve the linear system.
                      By using the calculator
                      a = 5.875 , b = -55.25 , c = 195

So, the quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
To predict the number of births for month 8
substitute with x = 8 ⇒ y = 5.875 * 8²- 55.25 * 8 + 195 = 129

Anew hospital tracked the number of births during its first 6 months of operation, as shown in the t

Anew hospital tracked the number of births during its first 6 months of operation, as shown in the t

answered: Guest

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

answered: Guest

The right answer is option d.