For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range.

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For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range.

Algebra
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f(x) is a polynomial function (why? cuz it has whole number powers of x only, and no other complex terms), and a polynomial is always continuous on the interval (-∞,+∞). that is for your domain.
the vertex of a parabola (your function is a parabola) in a form of: f(x)=a(x-h)²+k is the point: (h,k)

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Other answers:

can you identify the vertex here? \(f(x)=-2(x+3)^2-1\)
Is it (3, -1)?
almost.... \(f(x)=-2(x+3)^2-1\) \(f(x)=-2(x-\color{red}{-3})^2-\color{red}{1}\)
it is (-3,1)
and the domain is all real numbers (as I have reviously explained)
Now, your leading coefficient is negative, that means your parabola opens down and goes into -∞..... BUT, the range will be limited, and it is limited by the vertex because vertex is the maximum point (in any case when parabola opens down)
what is the y-value of your vertex? that is where the range ends.... and it starts from negative infinity
Wouldn't the range be y is equal to or lesser than -3
-3 is the x-coordinate of the vertex....
so not to -3, but to?
This it is -1
yes, the range is y≤-3
oh sorry
I mean y≤1
ok thank you
yw

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