You use the same principle

f'(x)=2ax+b

f'(-1)=0 <=>-2a+b=0 <=>b=2a

f(x)=ax^2+2ax+c

f(-1)=-4 and f(-4)=-8

a-2a+c=-4 and 16a-8a+c=-8

-a+c=-4 and 8a+c=-8

9a=-4 and -a+c=-4

a=-4/9 and c=-40/9

f(x)=-4/9x^2-8/9x-40/9

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