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.

mathtoo Aug 26, 2018

#1**+3 **

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)

CPhill Aug 26, 2018