Question 196014
f(x)=ax^2+bx+c

         f(0) = 6
a(0)^2+b(0)+c = 6
        0+0+c = 6
            c = 6

          f(-1) = 15
a(-1)^2+b(-1)+c = 15
          a-b+c = 15
          a-b+6 = 15 
            a-b = 15-6
            a-b = 9 -----> equ 1

           f(1) = 1
  a(1)^2+b(1)+c = 1
          a+b+c = 1
          a+b+6 = 1
            a+b = 1-6
            a+b = -5 -----> equ 2 

solve equ 1 and 2

           a-b = 9  (+)
           a+b = -5
           ---------
           2a  = 4
             a = 2
from equ 2
a+b = -5
2+b = -5
  b = -5-2
  b = -7

a = 2 ; b = -7 ; c = 6 
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check in f(1)=1

f(1) = 2(1)^2+(-7)(1)+6
     = 2-7+6
 f(1)= 1