15. find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). show your work.

y = -2(x -1)^2 -2

Step-by-step explanation:

My "work" consists of providing a table of values to a calculator and asking it for a quadratic model. The result is ...

y = -2(x -1)^2 -2

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If you like to do these "by hand", you can write the model, then solve for its parameters using the given points.

We observe that the first and third points have the same y-coordinate. Then the vertex of the quadratic will be halfway between the corresponding x-values, at ...

h = (-2 +4)/2 = 1

So, one of the parameters of the model is found already. Using the second point and one other, we can find the remaining parameters for our model:

y = a(x -1)^2 +k

for (4, -20) ...

-20 = a(4 -1)^2 +k = 9a +k

for (0, -4) ...

-4 = a(0 -1)^2 +k = a + k

Subtracting the second equation from the first, we get

-16 = 8a

-2 = a . . . . . divide by 8

Substituting this value of a into the second equation, we have ...

-4 = -2 +k

-2 = k . . . . . . add 2

So, our model is ...

y = -2(x -1)^2 -2

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify