+118724
$$y=a^2+6a-7$$
This is a concave up parabola (I can explain why if you ask)
$$y=(a+7)(a-1)$$
The roots are a=-7 and a=1
The axis of symmetry is a=(-7+1)/2 = -3
The minimum value
$$\\y=(-3)^2+6*(-3)-7\\
y=9-18-7\\
y=-16$$
The minimum value is -16
ALTERNATIVELY
It would have been easier to solve this using calculus. 
+118724
$$y=a^2+6a-7$$
This is a concave up parabola (I can explain why if you ask)
$$y=(a+7)(a-1)$$
The roots are a=-7 and a=1
The axis of symmetry is a=(-7+1)/2 = -3
The minimum value
$$\\y=(-3)^2+6*(-3)-7\\
y=9-18-7\\
y=-16$$
The minimum value is -16
ALTERNATIVELY
It would have been easier to solve this using calculus.
