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)