What is the value of b + c if x^2 + bx + c > 0 only when x is less than -4 or x is greater than 8?
+9479 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
