Question

Use technology to create an appropriate model of the data. (-1,0), (1,-4), (2,-3), (4,5), (5,12) f(x) = – x2 + 2x - 3 f(x) = x2 + 2x - 3 f(x) = – x2 - 2x - 3 f(x) = x2 - 2x - 3

Answer 1

Answer with explanation:

There are two ways of solving this question

→Plot the graph of each of the function given,and check whether all the points that is, (-1,0), (1,-4), (2,-3), (4,5), (5,12), lie on which curve and then find appropriate curve which fits the data.

→Second method is, by substituting value of ordered pair in the given function, for which function all different x value is equal to different y value.

Function 1:
`f(x)= -x^2+2 x-3`

`f(-1)= -(-1)^2+2*(-1)-3\\\\= -1-2-3\\\\-6`

so, the point (-1,0) does not lie on the curve. We do not need to check further.So, the function
`f(x)= -x^2+2 x-3` will not pass through all the data points.This is not the appropriate function for the set of given data points.

Function 2:
`f(x)= x^2+2 x-3`

`f(-1)= (-1)^2+2*(-1)-3\\\\= 1-2-3\\\\-4`

so, the point (-1,0) does not lie on the curve. We do not need to check further.So, the function
`f(x)= x^2+2 x-3` will not pass through all the data points.This is not the appropriate function for the set of given data points.

Function 3:
`f(x)= -x^2-2 x-3`

`f(-1)= (-1)^2-2*(-1)-3\\\\= 1+2-3\\\\=0`

`f(1)=-(1)^2-2(1)-3\\\\= -1-2-3\\\\=-6`

so, the point (1,-4) does not lie on the curve. We do not need to check further.So, the function
`f(x)= x^2+2 x-3` will not pass through all the data points.This is not the appropriate function for the set of given data points.

Function 4:
`f(x)= x^2-2 x-3`

`f(-1)= (-1)^2-2*(-1)-3\\\\= 1+2-3\\\\=3-3\\\\=0\\\\f(1)=(1)^2-2* 1-3\\\\=1-2-3\\\\=-4\\\\f(2)=2^2-2* 2-3\\\\=4-4-3\\\\=-3\\\\f(4)=4^2-2* 4-3\\\\=16-8-3\\\\=5\\\\f(5)=5^2-5* 2-3\\\\=25-10-3\\\\=12`

All the given set of points, (-1,0), (1,-4), (2,-3), (4,5), (5,12) lie on the curve
`f(x)= x^2-2 x-3`.

Function 4 ,
`f(x)= x^2-2 x-3`. is appropriate model for the given data set of points.

Option D

Answer 2

The appropriate choice seems to be ...

f(x) = x² -2x -3