Answer
Vertex: $(3,-4)$
Opens upward
x-intercepts: 1, 5
y-intercept: 5
Work Step by Step
$f(x)= x^2-6x+5$
$y=x^2-6x+5$
$y=(x^2-6x)+5$
$y=(x^2-6x)+5+(-6/2)^2-(-6/2)^2$
$y=(x^2-6x+(-6/2)^2)+5-(-6/2)^2$
$y=(x^2-6x+(-3)^2)+5-(-3)^2$
$y=(x^2-6x+9)+5-9$
$y=(x-3)^2-4$
Vertex: $(3,-4)$
Opens upward
$x=0$
$f(x)= x^2-6x+5$
$f(0)= 0^2-6*0+5$
$f(0)= 0-0+5$
$f(0)=5$
$y=0$
$y=(x-3)^2-4$
$0=(x-3)^2-4$
$0+4=(x-3)^2-4+4$
$4=(x-3)^2$
$\sqrt 4 = \sqrt {(x-3)^2}$
$±2 =x-3$
$-2=x-3$
$-2+3=x-3+3$
$1= x$
$2=x-3$
$2+3=x-3+3$
$5=x$
x-intercepts: 1, 5
y-intercept: 5
