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Question 1042694: Find the range of the function:
y=3x^2-6x+5
Help, are we supposed to tell the range just by looking at it?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It's possible by inspection but not easy here.
First, as x becomes large negative or large positive, x^2 will be positive, so the upper range is infinite.
The minimum value for the function is not obvious. The vertex is the lowest point, and it is at -b/2a, where b=-6 and a=3. Therefore, the x-value for the vertex is 6/6 or 1.
When x=1, 3x^2=3
When x=1, -6x=-6
when x=1, 5=5
The minimum value is 2.
The range is [2,oo)
Answer by ikleyn(52787)  (Show Source):
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