What is the minimum of y = -x^2- 6x - 7

No minimum.

Step-by-step explanation:

The equation of the parabola is given to be y = - x² - 6x - 7 (1)

Now, rearranging the equation we get  

y = - (x² + 6x + 9) - 7 + 9

⇒ y = - (x + 3)² + 2

⇒ y - 2 = - (x + 3)²

⇒ (x + 3)² = - (y - 2) (2)

Now, this equation is similar to the parabola equation (x - α)² = - 4a(y - β), which is the vertex form of a parabola equation.

Therefore, we can say that equation (2) has the vertex at (-3,2) and the axis is parallel to the negative y-axis.

Therefore, the parabola (1) has a maximum at (-3,2)  and it does not have a valid minimum. (Answer)

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation