Question 917349: Can you please explain how to find the vertex of this equation?
y^2-2x=2x-3
With solution please thanks Found 2 solutions by stanbon, rothauserc:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! find the vertex of this equation?
y^2-2x=2x-3
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4x = y^2 +3
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x = (1/4)y^2 + (3/4)
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Vertex occurs where y = -b/(2a)
y = (0/(1/2)) = 0
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f(0) = 0^2 + 3
x = f(0) = 3
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Vertex:: (3,0)
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Cheers,
Stan H.
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You can put this solution on YOUR website! y^2 -2x = 2x -3
add 2x to both sides of =
y^2 = 4x - 3
square root of both sides of =
y = square root(4x -3)
this is a parabola with a real part and an imaginary part
calculate the first derivative
dy/dx = (1/2) * (4x-3)^(1/2)
set first derivative to 0
(1/2) * (4x-3)^(1/2) = 0
multiply both sides of = by 2
(4x-3)^(1/2) = 0
square both sides of =
4x -3 = 0
x = 3/4
substitute x = 3/4 in y^2 = 4x - 3
y = 0
therefore the min point is
(3/4, 0)
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