Let f(x)=3x^2+6x-10For which input x is the value of the function a minimum?

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SUMMARY

The function f(x) = 3x² + 6x - 10 has a minimum value determined by the formula x = -b/2a, where a = 3 and b = 6. Since the coefficient of x² (a) is positive, the stationary point calculated using this formula indicates a minimum. The minimum occurs at x = -1, yielding a minimum value of f(-1) = -13. This confirms that for quadratic functions with a positive leading coefficient, the vertex represents the minimum point.

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Jurrasic
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And what is the minimum value?
( -b/2a is for a maximum problem, but how do you get through this kind of problem?)
 
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x=-b/2a will give you the stationary point for the quadratic. In f(x) =ax^2+bx+c, if a>0 is the stationary point maximum or minimum?
 
Jurrasic said:
And what is the minimum value?
( -b/2a is for a maximum problem, but how do you get through this kind of problem?)
For the quadratic, ax2 + bx + c:

If the coefficient of x2, which is a, is negative, then x = -b/2a, gives the x coordinate of the maximum.

If the coefficient of x2, which is a, is positive, then x = -b/2a, gives the x coordinate of the minimum.
 

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