Answer
$(0,3)$ and $(-6,3)$
Work Step by Step
To find the points of intersection of $f(x)$ and $g(x)$, set $f(x)=g(x)$ and solve the equation:
\begin{align*}x^2+6x+3&=3\\
x^2+6x&=0\\
x(x+6)&=0
\end{align*}
Use the Zero-Product Property by equating each factor to zero, then solve each equation::
\begin{align*}
x =0 \hspace{10pt} &\text{ or }& \hspace{10pt} x+6=0\\
x =0 \hspace{10pt} &\text{ or }& \hspace{10pt} x=-6
\end{align*}
To find the y-coordinates of the points of intersection, evaluate either of the two functions at $x=0$ and $x=-6$ to obtain:
$g(0)=3$
$g(-6)=3$
Therefore, the points of intersection are $(0,3)$ and $(-6,3)$.
