Question 64443
Graph f(x)= 3x^2-6x-1. plot at least 5 points. 
Of those 5 points, state the vertex point, whether the vertex point is maximum or minimum and the equation of axis of symmetry.
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If x=0 y=-1
If x=1 y=3-6-1=-4
If x=-1 y=3+6-1=8
If x=2 y==12-12-1=-1
If x=-2 y=12+12-1=23
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Complete the square to find the vertex and axis of symmetry:
3x^2-6x=y+1
3(x^2-2x)=y+1
x^2-2x=(1/3)(y+1)
Complete the square:
x^2-2x+1=(1/3)(y+1)+1
(x-1)^2=(1/3)(y+1+3)
(x-1)^2=(1/3)(y+4)
So, Vertex = (1,-4) is a minimum point because the parabola opens up.
Axis of symmetry is x=1
{{{graph(300,200,-10,10,-10,10,3x^2-6x-1)}}}
Cheers,
Stan H.