Answer: Choice D) x = -2(y+2)^2 - 3
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Step-by-step explanation:
One way to represent vertex form of sideways parabolas like this is to write
x-h = a(y-k)^2
where (h,k) is the vertex and 'a' determines how stretched out it is. All of the answer choices have a = -2, so we can ignore this value.
The vertex shown in the image is at (-3, -2). So this means (h,k) = (-3,-2) and furthermore h = -3 and k = -2.
Let's plug a = -2, h = -3 and k = -2 into the equation below and isolate x
x-h = a(y-k)^2
x-(-3) = -2(y-(-2))^2
x+3 = -2(y+2)^2
x = -2(y+2)^2 - 3
which is what choice D is saying