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Aloiza [94]
3 years ago
12

use a graphing calculator or other technology to answer the question which quadratic regression equation best fits the data set

?​

Mathematics
1 answer:
Greeley [361]3 years ago
3 0

Answer:

Option C is the correct option.

In other words, the quadratic regression y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\: best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation  y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:  is also attached.

Step-by-step explanation:

x                 y

3                470

4                416

5                403

Analyzing Option A:

Considering the equation

y=32.86\:\left(x\right)^2+379.14\left(x\right)-1369.14\:

From (3, 470), putting x = 3

y=32.86\:\left(3\right)^2+379.14\left(3\right)-1369.14\:

y=64.02

From (4, 470), putting x = 4

y=32.86\:\left(4\right)^2+379.14\left(4\right)-1369.14\:\:

y=673.18

From (5, 403), putting x = 5

y=32.86\:\left(5\right)^2+379.14\left(5\right)-1369.14\:

y=1348.06

Analyzing Option B:

y=32.86\:\left(x\right)^2-379.14\left(x\right)

From (3, 470), putting x = 3

y=32.86\:\left(3\right)^2-379.14\left(3\right)

y=-841.68

From (4, 470), putting x = 4

y=32.86\:\left(4\right)^2-379.14\left(4\right)

\:y=-990.8

From (5, 403), putting x = 5

y=32.86\:\left(5\right)^2-379.14\left(5\right)

\:y=-1074.2

Analyzing Option C:

Considering the equation

y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:

From (3, 470), putting x = 3

y=32.86\:\left(3\right)^2-379.14\left(3\right)+1369.14\:

y=527.46

So, the approximately result is (3, 527)

From (4, 470), putting x = 4

y=32.86\:\left(4\right)^2-379.14\left(4\right)+1369.14\:

y=378.34

So, the approximately result is (4, 378)

From (5, 403), putting x = 5

y=32.86\:\left(5\right)^2-379.14\left(5\right)+1369.14\:\:\:

y=294.94

So, the approximately result is (5, 295)

Analyzing Option D:

Considering the equation

y=-1369.14\:\left(x\right)^2-379.14\left(x\right)+32.86

From (3, 470), putting x = 3

y=-1369.14\:\left(3\right)^2-379.14\left(3\right)+32.86\:\:

y=-13426.82

From (4, 470), putting x = 4

y=-1369.14\:\left(4\right)^2-379.14\left(4\right)+32.86

y=-23389.94

From (5, 403), putting x = 5

y=-1369.14\:\left(5\right)^2-379.14\left(5\right)+32.86\:\:

y=-36091.34

Therefore, from the above calculations and analysis, we conclude that Option C is the correct option.

In other words, the quadratic regression y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\: best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation  y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:  is also attached.

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Answer:

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Step-by-step explanation:

Hi there!

We are given the points (-1, -3) and (-2, -5). We need to find the slope, equation of the line, and the y intercept of the line

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The formula for the slope (m) calculated from two points is \frac{y_2-y_1}{x_2-x_1} where (x_1,y_1) and (x_2,y_2) are points

We have everything we need for the formula, but let's label the values of the points to avoid any confusion

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Now substitute into the formula (remember: the formula has SUBTRACTION):

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simplify

m=\frac{-5+3}{-2+1}

add

m=\frac{-2}{-1}

divide

m=2

So the slope is <u>2</u>

Now let's find the equation of the line

The question asks for it to be in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We calculated the slope from earlier, so let's substitute that into the equation

y=2x+b

Now we need to find b

The equation will pass through both (-1, -3) and (-2, -5) so we can use either one of them to solve for b (doesn't matter which one)

Let's take (-1, -3) as an example

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multiply

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Add 2 to both sides

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Substitute -1 as b into the equation

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We found everything needed for this problem

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Step-by-step explanation:

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Step-by-step explanation:

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