Answer
$y \geq-\frac{2}{5} x^2-\frac{3}{5} x+1$
Work Step by Step
The $y$ intercept and the two points of the $x$ intercepts are clearly visible from the graph. These points can be used to find an equation of the parabola.
$y$- intercept: $(0,1)$
$x$ intercepts: $(-3,0),(1,0)$
\begin{equation}
\begin{aligned}
& f(x)=a x^2+b x+c \\
& f(0)=c=1
\end{aligned}
\end{equation} We determine $a$ and $b$: \begin{equation}
\begin{aligned}
f(x)& =a x^2+b x+1 \\
f(-3)& =9a-3b+1=0 \\
f(1) & =a+b+1=0
\end{aligned}
\end{equation} Now solve the system of equations for the values of $a$ and $b$. \begin{cases}
\begin{aligned}
9a-3 b & =-1 \\
a+b & =-1
\end{aligned}
\end{cases} Solve for $b$ in terms of $a$. \begin{equation}
\begin{aligned}
b & =-1-a \\
\end{aligned}
\end{equation} Substitute for $b$ in the first eq. and solve.
\begin{equation}
\begin{aligned}
9 a-3(-1-a) & =-1 \\
9+a+3 & =-1 \\
10 a & =-1-3 \\
10 a & =-4\\
a=\frac{-4}{10}\\
a=-\frac{2}{5}.
\end{aligned}
\end{equation} and \begin{equation}
\begin{aligned}
b & =-1-\left(-\frac{2}{5}\right) \\
& =-1+\frac{2}{5} \\
& =-\frac{5-2}{5} \\
& =-\frac{3}{5}.
\end{aligned}
\end{equation} The equation of the parabola is.
$$ f(x) = -\frac{2}{5}x^2-\frac{3}{5}x+1.$$ The graph of the quadratic function is sketched as a solid curve because there is a "equal to" part.
Now we have to find the inequality sign. We take a test point, for example $(0,0)$. The solution is the region which does not contain this point. We have:
$$\begin{aligned}
y&=0\\
-\frac{2}{5}x^2-\frac{3}{5}x+1&=-\frac{2}{5}(0^2-\frac{3}{5}(0)+1=1\end{aligned}
$$ As $0\leq 1$, we choose the opposite inequality sign, which is "greater or equal to" ($\geq$).
The inequality is: $$y\geq -\frac{2}{5}x^2-\frac{3}{5}x+1.$$
