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

1. anonymous

Is this multiple choice?

2. phi

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 $y = a x^2 + bx +c$

3. anonymous

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

4. phi

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)

5. phi

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

6. anonymous

x=1?

7. phi

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

8. anonymous

so f(x)=9?

9. phi

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.

10. anonymous

Oh so that is the final answer?

11. phi

yes

12. anonymous

Thank You!

13. phi

yw