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anonymous
 one year ago
If f(x)=3x^26x+12, then find the minimum value of f.
anonymous
 one year ago
If f(x)=3x^26x+12, then find the minimum value of f.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is this multiple choice?

phi
 one year ago
Best ResponseYou've already chosen the best response.2f(x)=3x^26x+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
 one year ago
Best ResponseYou've already chosen the best response.0What does it mean when it says "then find the minimum value of f."

phi
 one year ago
Best ResponseYou've already chosen the best response.2the f(x) (or "y" if we are plotting the curve on xy 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
 one year ago
Best ResponseYou've already chosen the best response.2the first step is find a and b (see up above) can you do that ?

phi
 one year ago
Best ResponseYou've already chosen the best response.2a= 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

phi
 one year ago
Best ResponseYou've already chosen the best response.2I 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
 one year ago
Best ResponseYou've already chosen the best response.0Oh so that is the final answer?
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