How do you find the vertex of a parabola given by the equation #x = y^2 - 4y + 3#?

1 Answer
Jim G.
Jul 7, 2018

#"vertex "=(-1,2)#

Explanation:

#"since the equation has a "y^2" term this indicates a"#
#"horizontal opening parabola with equation"#

#(y-k)^2=4a(x-h)#

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

#"to obtain this form "color(blue)"complete the square"#

#x=(y-2)^2-4+3#

#(y-2)^2=x+1#

#"with "h=-1" and "k=2#

#color(magenta)"vertex "=(-1,2)#
graph{x=y^2-4y+3 [-10, 10, -5, 5]}

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