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