Hello from MrBillDoesMath!
Answer:
Choice B is correct
Discussion:
Let y= -2(x+3)^2 - 2 (this is choice B)
The parabola in the diagram passes through the point (-3, -2). Does y? Let's check. Substitute x = -3 in the formula for y:
y = -2 ( -3+3)^2 - 2 = 0 - 2 = -2
so when x = -3, y = -2 and the parabola passes through (-3, -2)
Also note the first term of y is -2(x+3)^2, which is always negative or 0. This means that the parabola opens downward.
You can check the other choices, like I did for choice B, and you will find they fail at least one requirement (either not passing through (-3,-2), or opening the wrong way)
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!