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

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

Mathematics
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|dw:1440367057573:dw| That's the equation, right?
yes

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So simplify that. What's (x-1) squared?
x^2-2x+1
multiply that by 3 and what do you get
3x^2-6x+3
Oops, hold on. Sorry, you didn't have to do all that. For the vertex, since you have (x-1), plug in 1 for x in the original equation. What is your y value?
2
So your vertex would be (1,2).
ya I know that but what is the range
As for domain, are there any values that you can't plug in for x? As for the range, are there any values that you can't get for y?
i have no idea :/
Well, you can plug in just about everything for x, so the domain would be (-infinity, infinity). As for range, you can get a y value that is above 2, the y-value in your vertex. So it would be [2, infinity}

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