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y = -x² + 4x - 1

multiplying both sides of the equation with -1

-y = x² - 4x + 1

transposing 1 to the left side:

-y - 1 = x² - 4x or

x² - 4x = -y - 1

complete the square for x by adding 4 to both sides of the equation:

x² - 4x + 4 = -y - 1 + 4

factor the quadratic expression

(x - 2)² = -y + 3

factor -1 from the right side:

(x - 2)² = -(y - 3)

this now follows the standard equation for parabola whose x is quadratic and y is linear.

(x - h)² = 4a(y - k)

where (h,k) are the coordinates of the vertex

therefore the vertex is at (2,3)