Question 523603
(x-4)^2 = 4(y-1)
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x^2 -8x + 16 = 4y -4
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4y-4 = x^2 -8x + 16
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4y = x^2 -8x +20
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y = (1/4)*x^2 -2x + 5
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{{{ graph(500,500,-10,10,-20,20,1/4*x^2-2*x+5) }}}
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You will notice the parabola does not cross or touch the x-axis, so there are no solutions with real numbers.  You can confirm this with the quadratic equation.
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*[invoke quadratic "x", 1/4, -2, +5 ]