Answer
$(-1,-1)$ and $\left(-\dfrac{1}{2},\dfrac{1}{2}\right)$
Work Step by Step
To find the points of intersection of $f(x)$ and $g(x)$, solve $f(x)=g(x)$:
\begin{align*}
-2x^2+1&=3x+2\\
0&=2x^2-1+3x+2\\
0&=2x^2+3x+1
\end{align*}
By Factoring:
$$0=(x+1)(2x+1)$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation:
\begin{align*}
x+1 &=0 &\text{ or }& &2x+1=0\\
x &=-1 &\text{ or }& &2x =-1\\
x &=-1 &\text{ or }& &x=-\dfrac{1}{2}\\
\end{align*}
To find the y-coordinates of the points of intersection, evaluate either of the two functions at $x=-1$ and $x=-\dfrac{1}{2}$ to obtain:
$g(-1)=3(-1)+2=-1$
$g(-\dfrac{1}{2})=3(-\dfrac{1}{2})+2=\dfrac{1}{2}$
Therefore, the points of intersection are $(-1,-1)$ and $\left(-\dfrac{1}{2},\dfrac{1}{2}\right)$.
