Answer
$\left(-6,3 \right)$ and $\left(4,33\right)$
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+5x-3&=2x^2+7x-27\\
0&=-x^2-5x+3+2x^2+7x-27\\
0&=x^2+2x-24
\end{align*}
By Factoring:
$$0=(x+6)(x-4)$$
Use the Zero-Product Property by equating each factor to zero,then solve each equation to obtain:
\begin{align*}
x+6 &=0 &\text{ or }& &x-4=0\\
x &=-6 &\text{ or }& &x =4\\
\end{align*}
To find the y-coordinates of the points of intersection, evaluate either of the two functions at $x=-6$ and $x=4$ to obtain:
$f(-6)=(-6)^2+5(-6)-3=3$
$f(4)=(4)^2+5(4)-3=33$
Thefore, the points of intersection are:
$\left(-6,3 \right)$ and $\left(4,33\right)$
