SOLUTION: without graphing, fing the minimum value f(x)=3(x+12.68)^2-sqrt22

Algebra ->  Coordinate-system -> SOLUTION: without graphing, fing the minimum value f(x)=3(x+12.68)^2-sqrt22      Log On


   

Question 210385: without graphing, fing the minimum value
f(x)=3(x+12.68)^2-sqrt22
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Without graphing, to find the minimum value, you need to look at the terms and see which one(s) can change. You know that sqrt%2822%29 is a constant, so that one won't change. You can see that the first term 3%28x%2B12.68%29%5E2 involves a factor of that includes a square. You know that the minimum a squared value can be is 0 (A squared value is always going to be positive or 0).
So the minimum value occurs when the first term is 0.
So what value of x makes 3%28x%2B12.68%29%5E2=0
x+=+-12.68
When x = -12.68, then f%28x%29+=+0+-+sqrt%2822%29+=+-sqrt%2822%29