Answer:
Choice A
Min value: -4
Domain: All real numbers
Range: All real numbers greater than or equal to -4
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The given equation y = 2(x-3)^2-4 is in the form y = a(x-h)^2 + k
a = 2 is the leading coefficient
since the leading coefficient is positive, the graph opens upward meaning this graph has a min value (instead of a max). Since we know it doesn't have a max, we can rule out choice B and choice C
The min value is the value of k, which in this case is k = -4. At this point, we can see the answer is choice A. Recall that (h,k) is the vertex which is either the highest or lowest point.
Adding on more confirmation that the answer is choice A, the domain is in fact the set of all real numbers. We can replace x with any number want to get some output value for y. There are no restrictions since we don't have to worry about dividing by zero or taking the square root of a negative number.
The range is the set of y values such that y >= -4. Basically y is either -4 or larger than -4. This comes from the fact that y = -4 is the smallest output possible (aka the min value mentioned earlier)
