since this is a parabola with x being quadratic and y being linear then we'll have:
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)
