For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.
The vertex is (–1, 2), the domain is all real numbers, and the range is y ≥ 2.
The vertex is (–1, 2), the domain is all real numbers, and the range is y ≤ 2.
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Hi there :)
Sorry for being a little late to respond .-.
they have given you the equation in "vertex form"
where \( f(x) = a(x-h)^2+k \)
where the point \( (h,~k) \) is the vertex
comparing this "form" to your \( f(x) = 3(x-1)^2 + 2 \)
we can see that \( h=1 \) and \(k=2\)
putting this as a point \((h,k)\), you would get the proper vertex point that they are asking for :)
The other deciding factor in your options, it seems, would be the range.
If you have seen a picture of a \(parabola\) before [it looks like a U]
from this we can say that anything above the vertex (in this case) would be included in the range
so since we got that the y value of the vertex to be \(k=2\)
we can say that the range of this function would be greater than and including \(2\)