Answer
$(-2,-60)$ .
Work Step by Step
Given $$
\begin{cases}
& y=5 x^2+20 x-40 \\
& y=-3 x^2-12 x-72.
\end{cases}
$$ Set the two equations equal and solve for the values of $x$.
$$
\begin{aligned}
5 x^2+20 x-40 & =-3 x^2-12 x-72 \\
5 x^2+3 x^2+20 x+12 x & =40-72 \\
8 x^2+32 x & =-32 \\
x^2+4 x & =-4\\
x^2+4x +2^2&= -4+2^2\\
(x+2)^2&= 0\\
x&= -2.\end{aligned}
$$ Find the corresponding $y$ values using either of the given equations.
$$
\begin{aligned}
y&= 5(-2 )^2+20\cdot( -2) -40\\
& = -60.
\end{aligned}
$$ Plot the two functions in the same window to check the solution(s).
The solution is $(-2,-60)$.
