Answer
$(0,3)$ and $(4,3)$
Work Step by Step
To find the points of intersection of $f(x)$ and $g(x)$, solve $f(x)=g(x)$ $$x^2-4x+3=3$$ $$x^2-4x=0$$ Taking $x$ as a common factor:
$$x(x-4)=0$$
Use the Zero-Product Property by equating each factor to zero, then solve:
\begin{align*}
x =0 \hspace{10pt} &\text{ or } \hspace{10pt} x-4 =0\\
x =0 \hspace{10pt} &\text{ or } \hspace{10pt} x =4\\
\end{align*}
To find the y-coordinates of the points of intersection, evaluate either of the two functions at $x=0$ and $x=4$ to obtain:
$g(0)=3$
$g(4)=3$
Therefore, the points of intersection are $(0,3)$ and $(4,3)$
