(x + 5)^2 + 3

parabola

x^2 + 10 x + 28

x (x + 10) + 28

(-i x + sqrt(3) - 5 i) (i x + sqrt(3) + 5 i)

x = -5 - i sqrt(3)

x = -5 + i sqrt(3)

Δ = -12

R (all real numbers)

{y element R : y>=3}

d/dx((x + 5)^2 + 3) = 2 (x + 5)

integral(3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + constant

min{(x + 5)^2 + 3} = 3 at x = -5