Answer:

Step-by-step explanation
Let equation be 

Since (-4,9) satisfy the  equation ,plugging x =-4 and f(x) = 9 

  9 = 16a -4b +c  ........ equation 1 
 plugging x =0 and f(x) = -7 
-7 = a(0) +b(0) +c 
gives c =-7 ......... equation 2
plugging x =1 and f(x) =-1 
-1 = a(1) + b(1) +c 
-1 = a+b+c ............. equation 3 
From equation 2 ,we have c =-7 
Plugging this value in equation in 1 and 3 ,we get 
16a -4b -7 =  9
16a-4b= 9+7 
16a-4b = 16 
Dividing the equation by 4 ,we get 
        4a -b = 4  ..........  equation 4
Plugging c =-7 in equation 1 ,we get 
a+b+(-7) = -1 
a+b = -1+7 
a+b = 6 ......... equation5 
Adding equation 4 and equation 5 
  a+b =6 
4a-b =4  
______________
5a = 10 
a = 2 
plugging a =2 in equation2 
2+b = 6 
  b = 6-2 
  b = 4 
therefore quadratic equation is 
