What is the vertex of # y=x^2-2x+1 #?
2 Answers
( 1 , 0 )
Explanation:
The standard form of the quadratic function is
#y =ax^2+bx+c # The function
# y = x^2 - 2x + 1 " is in this form "# with a = 1 , b = -2 and c = 1
the x-coordinate of the vertex can be found as follows
x-coord of vertex
# = - b/(2a )= -(-2)/2 = 1 # substitute x = 1 into equation to obtain y-coord.
# y = (1)^2 -2(1) + 1 = 0 # thus coordinates of vertex = (1 , 0)
#"--------------------------------------------------------------------"# Alternatively : factorise as
#y = (x - 1 )^2# compare this to the vertex form of the equation
# y = (x - h )^2 + k " (h,k) being the vertex " # now
#y = (x-1)^2 + 0 rArr " vertex " = (1,0)#
graph{x^2-2x+1 [-10, 10, -5, 5]}
Vertex
Look at https://socratic.org/s/aMzfZyB2 for detailed determination of the vertex by 'completing the square'.
Explanation:
Compare to standard form of
Rewrite as:
In your case
Substitute for x=1
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