Steps:
1) we calculate the first derivative:
y´=2x+8
2) we calculate the value of "x" when the first derivative is equal to "0",
2x+8=0
2x=-8
x=-8/2
x=-4
3) we calculate the second derivative:
y´´=2; then , becuse y´´>0; we have a minimun at x=-4
4)we calculate the value of "y".
y=f(-4)=(-4)²+8*(-4)+3=-13
Answer: the minimun is found in (-4,-13)