Question 183003
I need to find the axes, roots, and the vertices of the 3 following questions. Can you please show it to me in the completing the square method. 
The questions are
y=2x^2-x+6
2x^2 - x + ? = y-6+?
2(x^2 - (1/2)x + (1/4)^2 = y - 6 + 2(1/4)^2
2(x- (1/4))^2 = y - (48/8) + (1/8)
2(x-(1/4)^2 = y - (47/8)
(x - (1/4)^2 = (1/2)(y -(47/8))
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Vertex: (1/4 , (-47/8))
vertical axis: x = 1/4
Roots: No Real roots
Use Quadratic formula to find the complex roots.
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y=x^2-8x+2
x^2 - 8x = y-2
x^2 - 8x + 16 = y -2 + 16
(x-4)^2 = y + 14
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Vertex: (4 , -14)
vertecal axis: x = 4
Roots: Use the quadratic formula.
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y=4x^2-x+1
4x^2 - x = y - 1
4(x^2 - (1/4)x + (1/8)^2) = y - 1 + 4*(1/8)^2
4(x - (1/8))^2 = y - 15/16
(x-(1/8))^2 = (1/4)(y - 15/16)
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Vertex: (1/8 , 15/16)
vertical axis: x = 1/8
Roots: Use the Quadratic formula
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Cheers,
Stan H.