Chapter 9 - Solving Quadratic Equations - 9.4 - Solving Quadratic Equations by Completing the Square - Exercises - Page 512: 47

Yes

$$y=-(x+8)(x+3)$$ Here the graph of this function will open down as $a<0$ and it has a maximum value. Also it has two negative $x$-intercepts meaning the vertex is in the second quadrant. So the given graph could represent the function.