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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    Is this multiple choice?

  2. phi
    • one year ago
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    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
    • one year ago
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    What does it mean when it says "then find the minimum value of f."

  4. phi
    • one year ago
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    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
    • one year ago
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    the first step is find a and b (see up above) can you do that ?

  6. anonymous
    • one year ago
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    x=1?

  7. phi
    • one year ago
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    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
    • one year ago
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    so f(x)=9?

  9. phi
    • one year ago
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    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
    • one year ago
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    Oh so that is the final answer?

  11. phi
    • one year ago
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    yes

  12. anonymous
    • one year ago
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    Thank You!

  13. phi
    • one year ago
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    yw

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