# Determine without graphing

Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+30x-1

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posted by Reiny
2. I needed help learning how to find the value.

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posted by Jenn
3. f(x) = 3(x^2 + 10x +25)-76
= 3(x+5)^2 -76

The function has no maximum. It has a minimum of -76 when x = -5.

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posted by drwls
4. Hmmm. I explained that there is no maximum value. Don't expect to be able to find it.

Now, if you want to find the minimum value, try completing the square:

3x^2+30x-1
= 3(x^2 + 10x) - 1
= 3(x^2 + 10x + 25) - 1 - 75
That step is the key. We added 75 to complete the square, so we have to subtract it as well to avoid changing f(x)
= 3(x+5)^2 - 76

Now you can see that since (x+5)^2 is always at least zero (since squares are never negative), the smallest value for (x+5)^2 is when x = -5. In that case, f(x) = 3(0) - 76

So, f(-5) = -76, and it can never be less than that, because whatever x is, (x+5)^2 will be some positive number, making f(x) > -76

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posted by Steve

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