Answer:
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)
