what property was used to find x- intercept 0=(x-5)(x-1)

Provided, f ( x ) = x 2 - 6* + 5 Find: Graph the function Solution : Intercepts : . X - intercept : Set y = 0 ; 0 = X - 6x+ 5.0 01 = ( x- 5 ) ( x - 1 ) Thus, x = 5 8 X = 1 . Y - intercept : Set X = 0 4 = 0 - 6(0)+5 y = 5 Vertex: Find first derivative: f ( x ) = 2 x - 6 = 0 X = 3 @ X = 3 f ( 3 ) = 3 - 6 ( 3 ) + 5 = - 4 Therefore ; y- axis ( 0 , 5 ) ( 1 , 0 ) X - axis ( 510 ) ( 3 , - 4 )