Answer
$(-3,-29)$
Work Step by Step
Given $$
\begin{cases}
& y=x^2+6 x-20 \\
& y=-x^2-6 x-38.
\end{cases}
$$ Set the two equations equal and solve for the values of $x$. $$
\begin{aligned}
x^2+6 x-20 & =-x^2-6 x-38 \\
x^2+x^2+6 x+6 x & =20-38 \\
2 x^2+12x & =-18 \\
2 x^2+12x+18 & =0
\end{aligned}
$$ $$
\begin{aligned}
& a=2 \\
& b=12\\
& c=18
\end{aligned}
$$ $$
\begin{aligned}
x& =\frac{-12 \pm \sqrt{12^2-4 \cdot 2 \cdot 18}}{2 \cdot 2}\\
x& =\frac{-12 \pm \sqrt{0}}{4}\\
x&= -3.
\end{aligned}
$$
Find the corresponding $y$ values using either of the given equations. $$
\begin{aligned}
y&= (-3 )^2+6\cdot( -3) -20\\
& = -29.
\end{aligned}
$$
Plot the two functions in the same window to check the solution(s).
The solution is $(-3,-29)$.
