+816 For what values of b is -2 not in the range of the function \(f(x)=x^2+bx+2\)? Express your answer in interval notation.
+128475 x^2 + bx + 2
This parabola turns upward....so...the x coordinate of the vertex is given by
-b/ 2 = x
So....we'd ike to solve this
(-b/2)^2 + b(-b/2) + 2 > - 2 simplify
b^2/4 - b^2/2 + 4 > 0
-b^2/4 + 4 > 0
-b^2 + 16 > 0 multiply through by -1 and change the inequality sign
b^2 - 16 < 0
(b - 4) ( b + 4) < 0
The values that make this true are ( -4, 4)
So...the values that put -2 out of range are (-4, 4)
