Answer
See graph,
vertex $(0.5,2)$, axis $x=0.5$,
no x-intercept, y-intercept $(0,3)$,
domain $(-\infty,\infty)$, range $[2,\infty)$, increasing $(0.5,\infty)$, decreasing $(-\infty,0.5)$.
Work Step by Step
Step 1. Graph the function $f(x)=4x^2-4x+3=(2x-1)^2+2$ as shown in the figure.
Step 2. We can identify the vertex $(0.5,2)$, axis $x=0.5$,
Step 3. For x-intercepts, let $f(x)=0$, we have $(2x-1)^2+2=0$, no real solution thus no x-intercept. For y-intercept, we have $f(0)=3$ or $(0,3)$,
Step 4. We can find domain $(-\infty,\infty)$, range $[2,\infty)$, and largest open intervals of the domain over which each function is increasing $(0.5,\infty)$, decreasing $(-\infty,0.5)$.