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What is the minimum value of the function y=x^2-4x-5

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What is the minimum value of the function y=x^2-4x-5 [#permalink] New post 19 Jan 2012, 16:08
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What is the minimum value of the function y=x^2-4x-5?
Can someone explain how to approach this one?
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Re: What is the minimum value of the function y=x^2-4x-5 [#permalink] New post 19 Jan 2012, 17:19
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Splendidgirl666 wrote:
What is the minimum value of the function y=x^2-4x-5?
Can someone explain how to approach this one?


We can solve this one with parabola function approach, though I think the following will be easier:

y=x^2-4x-5=(x^2-4x+4)-9=(x-2)^2-9, now as (x-2)^2\geq{0} (so min value is 0) then the minimum value of the function is 0-9=-9.

P.S. ALWAYS post answer choices for PS questions.
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Re: What is the minimum value of the function y=x^2-4x-5 [#permalink] New post 20 Jan 2012, 22:11
If you are at all familiar with calculus taking the derivative setting it = 0 and plugging in values may be easier here. Just remember that if you only get one value you need a second derivative test to check whether it is a min or a max.
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Re: What is the minimum value of the function y=x^2-4x-5 [#permalink] New post 21 Jan 2012, 01:32
Expert's post
joeshmo wrote:
If you are at all familiar with calculus taking the derivative setting it = 0 and plugging in values may be easier here. Just remember that if you only get one value you need a second derivative test to check whether it is a min or a max.


Yes, you can use derivative for this: y'=2x-4 --> 2x-4=0 --> x=2 --> substituting this value in the original expression we'll get: x^2-4x-5=4-8-5=-9.

As for the second part of your post: as the coefficient of x^2 in x^2-4x-5 is positive then this function will have ONLY minimum value and not maximum, so no need for further checking (y=x^2-4x-5 is an upward parabola and the minimum of this function is y-coordinate of its vertex). Check for more on parabolas in Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Also note that derivative of a function is not tested on the GMAT.
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Re: What is the minimum value of the function y=x^2-4x-5 [#permalink] New post 05 Mar 2014, 23:06
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Re: What is the minimum value of the function y=x^2-4x-5   [#permalink] 05 Mar 2014, 23:06
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