SOLUTION: Find the range of the function:
y=3x^2-6x+5
Help, are we supposed to tell the range just by looking at it?
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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(52788) (Show Source): You can put this solution on YOUR website!
.
Find the range of the function:
y=3x^2-6x+5
Help, are we supposed to tell the range just by looking at it?'
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
No, you are supposed to find the minimum of this quadratic function.
The procedure is as follows.
First find the value of "x" where the minimum occurs.
For the general quadratic function y = the minimum is at x = .
In your case it is x = = 1.
Now, to find the value of the minimum for "y" (the value of the minimum of the function),
substitute this x=1 into the quadratic function.
You will get = = 3 - 6 + 5 = 2.
Now compare it with the plot below.
Now the answer to the question about the range is: [,).
It is a semi-infinite segment from 2 to infinity. The value of 2 is included into the segment.
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