Was ist der Eckpunkt von # y = x ^ 2-2x + 1 #?
Antworten:
(1, 0)
Erläuterung:
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]}