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

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0f(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.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0the vertex of a parabola (your function is a parabola) in a form of: f(x)=a(xh)²+k is the point: (h,k)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0can you identify the vertex here? \(f(x)=2(x+3)^21\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0almost.... \(f(x)=2(x+3)^21\) \(f(x)=2(x\color{red}{3})^2\color{red}{1}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0and the domain is all real numbers (as I have reviously explained)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Now, 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)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0what is the yvalue of your vertex? that is where the range ends.... and it starts from negative infinity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't the range be y is equal to or lesser than 3

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.03 is the xcoordinate of the vertex....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0so not to 3, but to?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, the range is y≤3
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