A quadratic patteen haa a second term equal to 1 at third term equal, to - 6 and a fifth term, equal to - 14

Y=ax^2+bx+c

25a+5b+c=-14

9a+3b+c=-6

4a+2b+c=1 getting differences ...

16a+2b=-8

5a+b=-7 (10a+2b=-14) differences again ...

6a=6, so a=1 making 16a+2b=-8 become:

16+2b=-8, so b=-12 making 4a+2b+c=1 become:

4-24+c=1, so c=21 so our quadratic is:

y=x^2-12x+21