<p>Let the function p be defined by p(x)= a(x-k)^2 , where a and k are positive constants. For what value of x will the function p have its minimum value?</p>
<p>A. -a
B. -k
c. 0
D. a
E. k</p>
<p>what minimum value?</p>
<p>The minimum value something can have is just the smallest possible number it could be. For example, the minimum value you can have on the math section on the SAT is a 200.</p>
<p>I'll let you reason it out.
Is it possible for p to be a negative number?
If so, how?
If not, why not?
We're looking for p as the smallest it can be.
What value can p be, then, that's as small as possible?
If p is that value, then what does x have to be?</p>
<p>OOOOO, so its E because 0 is the smallest since negatives arnt possible (a and k are positive constants) , thus it must be K.</p>
<p>Im not gay, but I love you <3 I spent nearly an hour pondering over this question lol.</p>
<p>omg lol,u have time =) 1 hr T_T?</p>
<p>its quite obvious when u see a=positive, and square.</p>
<p>I would probably plug in numbers for this cause I dont get it. Is that a wrong thing to do?</p>
<p>Well, given that it's a multiple choice test and "none of the above" isn't an option, you could plug in the values you are given. It would take longer, though, so your best move on the actual test if you were going to employ this method would be to skip it and go back later after you'd answered everything you can answer quickly.</p>
<p>If it weren't a multiple choice test or if "none of the above" were an option, it wouldn't be a good approach: you might get it if you were lucky and one of the values you plugged in was k, but you might be unlucky too.</p>
<p>The thing about the SAT is that it's a timed test, so they can't give you a problem that takes a long time to solve. Therefore if you can't figure it out (and you've answered all the questions you can answer quickly), you should look at it and ask yourself why they gave you the information that they did. For one thing, a is positive and (x-k)^2 is nonnegative; the lowest value you can get when multiplying a positive number by a nonnegative number is 0. Well, a is positive, and 0 divided by a positive number is 0, and the square root of 0 is 0 as well, so x - k = 0. And that means that x = k.</p>
<p>I guess if you realize that it HAS to be positive since the constants are positive, you can figure out thats it must be k right away. Questions dealing with minimum value scared me until now. Thanks for all the input guys.</p>
<p>so what is the answer?</p>
<p>"you can figure out thats it must be k right away"</p>
<p>" 0 is 0 as well, so x - k = 0. And that means that x = k."</p>
<p>"since negatives arnt possible (a and k are positive constants) , thus it must be K."</p>
<p>I wonder.</p>
<p>The answer is quite obvious. (E)</p>
<p>to nontraditional. ur absolutely right. Its more logic than math.</p>