Answer and Step-by-step explanation:
The answer is the last answer choice.
g(x) = [tex]-(x + 2)^2 + 1[/tex]
We don't even have to look at the numbers to tell that this is the correct answer. We look at what is being placed there.
The equation for a transformed function is:
f(x) = [tex]a(x-h)^2 + k[/tex]
a determines the scale of the graph and whether the graph opens up or down.
h determines whether the graph shifts left or right.
k determines whether the graph shifts up or down.
We see that there is a -1 for a, which means the graph will be facing downwards. We see a 2 for where h is, but it really is a -2, and when it becomes a positive after simplifying, the graph will shift to the left.
k is a positive 1, so the graph will be shifted up 1 unit.
Thus, the answer is the last answer choice.
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