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A parabola with equation $y=x^2+bx+c$ passes through the points $(-1,-11)$ and $(3,-17)$. What is $c$?

 Aug 9, 2023
 #1
avatar+129659 
+1

We have these equations

 

-11 = (-1)^2 + b(-1) + c

-17 = (3)^2 + b(3) +  c   simplify

 

-11 = 1 -b + c

-17=  9 + 3b + c

 

-12 = -b + c

-26 = 3b + c       subtract  these

 

14 = -4b

 

14/ -4 = b =  -7/2

 

And we can  find  c as

 

-12 = - (-7/2) + c

-12  = 7/2 + c

-12 - 7/2  = c = -24/2 - 7/2 =    -31/2

 

 

cool cool cool

 Aug 9, 2023

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