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

We have this

(-1)^2 + b(-1)  + c  = -11

(3)^2 + b(3)  + c   =  17

So we have

1 - b  +  c  =  -11

9 + 3b +  c  = 17

-b +  c  =  -12       multiply through by -1  =  b - c  = 12     (1)

3b +  c   = 8       (2)

Add (1)  and (2)

4b  =  20     divide both sides by 

b  = 5

And using (1)

5 - c  = 12    ⇒    c =  -7