For what constant k is -1 the minimum value of the quadratic 4x^2-12x+k+x^2+2x over all real values of x? x can not be unreal
Rearrange as
4x^2 +x^2 -12x + 2x + k
5x^2 - 10x + k
The x coordinate of the vertex of this parabola is -(-10) / (2 *5) = 10 / 10 = 1
So...we want
5(1)^2 - 10 (1) + k = - 1
5 -10 + k = -1
-5 + k = -1
k = -1 + 5 = 4
