An equation that models the data is: y=(x^3)/2-2x^2+9x/2+1.
To find the equation I used the fact that there are 4 data pairs and I can find 4 unknowns from 4 equations.
I also know that if the ordered pair is (x,y), y increases with x, and y is defined for x in {0, 1, 2, 3}.
Let y=ax^3+bx^2+cx+d. This equation has 4 unknown coefficients a to d.
When x=0, y=1 so d=1.
When x=1, y=4 so a+b+c+d=4 and a+b+c=3. c=3-(a+b).
When x=2, y=6 so 8a+4b+2c+d=6 and 8a+4b+2(3-(a+b))=5. 6a+2b=-1, and b=-(6a+1)/2. Therefore c=3-(a-(6a+1)/2)=(4a+7)/2.
When x=3, y=10 so 27a+9b+3c+1=10 and 27a-9(6a+1)/2+3(4a+7)/2=9.
54a-9-54a+12a+21=18 and 12a=6, so a=1/2.
From a=1/2 we get b=-2 and c=9/2.
If we substitute the data pairs we find that they satisfy the equation y=(x^3)/2-2x^2+9x/2+1.
Therefore this equation models the data.