Answer
$\left(-3,13 \right)$ and $\left(5,21\right)$
Work Step by Step
To find the points of intersection of $f(x)$ and $g(x)$, solve $f(x)=g(x)$:
\begin{align*}
x^2-x+1&=2x^2-3x-14\\
0&=-x^2+x-1+2x^2-3x-14\\
0&=x^2-2x-15
\end{align*}
By Factoring:
$$0=(x+3)(x-5)$$
Use the Zero-Product Property by equating each factor t zero, then solve each equation to obtain:
\begin{align*}
x+3 &=0 &\text{ or }& &x-5=0\\
x&=-3 &\text{ or }& &x=5\\
\end{align*}
To find the $y$-coordinates of the points of intersection, evaluate either of the two functions at $x=-3$ and $x=5$ to obtain:
$f(-3)=(-3)^2-(-3)+1=13$
$f(5)=(5)^2-(5)+1=21$
Therefore, the points of intersection are:
$\left(-3,13 \right)$ and $\left(5,21\right)$
