What is the value of b + c

The graph of  y = x² + bx + c  is a parabola that opens upward and intersects the x-axis at  -4  and  8 .

 

An equation for a parabola that opens upward and intersects the x-axis at  -4  and  8  is  y = (x + 4)(x - 8)

 

Let's take the second equation and expand the right side by FOILing it:

 

y  =  (x + 4)(x - 8)

 

y  =  x² - 4x - 32

 

Now we can see that  x² - 4x - 32  matches  x² + bx + c  and so we can say...

 

b = -4

c = -32

 

b + c = -36

 

Here's a graph of that parabola expressed both ways: https://www.desmos.com/calculator/afkj6kil8d