Question 138847
GIVEN THE FUNCTION DEFINED BY: f(x)=x^2-6x+12
A) IDENTIFY THE VERTEX OF THE PARABOLA.
You have a quadratic with a=1 , b=-6, and c = 12
The vertex occurs where x = -b/2a = 6/2 = 3
The corresponding y-value is f(3) = 9-18+12 = 3
The vertex is (3,3)
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B)DOES THIS PARABOLA OPEN UP OR DOWN?
Since the coefficient of the x^2 term is positive, the parabola
opens upward.
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C)DOES THE VERTEX REPRESENT THE MAXIMUM OR MINIMUM POINT OF THE FUNCTION?
Because of what is said in part B, the vertex is a minimum point.
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D)WHAT IS THE MAXIMUM OF MINIMUM VALUE OF THE FUNCTION f?
There is no maximum f value; the minimum value is 3 which occurs where x=3.
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E) WHAT IS THE AXIS OF SYMMETRY FOR THIS PARABOLA?
The axis of symmetry is the vertical line thru the vertex, or x = 3.

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{{{graph(400,300,-10,10,-10,20,x^2-6x+12)}}}
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Cheers,
Stan H.