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

The appropriate choice seems to be ...

f(x) = x² -2x -3

Answer 2

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: $f(x)= -x^2+2 x-3$

        $f(-1)= -(-1)^2+2\times(-1)-3\\\\= -1-2-3\\\\-6$

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: $f(x)= x^2+2 x-3$

        $f(-1)= (-1)^2+2\times(-1)-3\\\\= 1-2-3\\\\-4$

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: $f(x)= -x^2-2 x-3$

        $f(-1)= (-1)^2-2\times(-1)-3\\\\= 1+2-3\\\\=0$

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

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: $f(x)= x^2-2 x-3$

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

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