If f(x)=3x^2-6x+12, then find the minimum value of f.

Question

anonymous · Answer

Is this multiple choice?

phi · Answer

f(x)=3x^2-6x+12

that is the equation of a parabola with the shape $\cup$
and its minimum is at its vertex.

the x value of the vertex is at 
$$ x = \frac{-b}{2a} $$
where a , b and c are found by matching your parabola equation to
$$ y = a x^2 + bx +c $$

anonymous · Answer

What does it mean when it says "then find the minimum value of f."

phi · Answer

the f(x)  (or "y" if we are plotting the curve on x-y graph)
is smallest at the vertex.  they want the f(x) value.

to find it,  first find the x value of the vertex (see above)
then use that number in your parabola formula to find f(x) at the vertex (which will be the min that you want)

phi · Answer

the first step is find  a and b (see up above)
can you do that ?

anonymous · Answer

x=1?

phi · Answer

a= 3  ,  b= -6
-b/(2a)  is  -(-6)/(2*3) = 6/6 = 1
yes  x=1

now use x=1 in the formula to find the f(x) value

anonymous · Answer

so f(x)=9?

phi · Answer

I guess we should write it 
f(1)= 9
(which means at x=1,  the function has the value 9)

anyway, 9 is the smallest this parabola gets.

anonymous · Answer

Oh so that is the final answer?

phi · Answer

yes

anonymous · Answer

Thank You!

phi · Answer

yw