1. The problem is to graph the quadratic function $y = x^2 + 5x + 6$. 2. The general form of a quadratic function is $y = ax^2 + bx + c$. Here, $a=1$, $b=5$, and $c=6$. 3. To understand the graph, find the roots by factoring: $$x^2 + 5x + 6 = (x + 2)(x + 3)$$ So, the roots are $x = -2$ and $x = -3$. 4. The vertex can be found using the formula for the x-coordinate: $$x = -\frac{b}{2a} = -\frac{5}{2 \times 1} = -\frac{5}{2} = -2.5$$ 5. Substitute $x = -2.5$ into the function to find the y-coordinate of the vertex: $$y = (-2.5)^2 + 5(-2.5) + 6 = 6.25 - 12.5 + 6 = -0.25$$ 6. The vertex is at $(-2.5, -0.25)$, which is the minimum point since $a > 0$. 7. The y-intercept is found by evaluating $y$ at $x=0$: $$y = 0^2 + 5 \times 0 + 6 = 6$$ 8. Summary: The parabola opens upward, crosses the x-axis at $-3$ and $-2$, has vertex at $(-2.5, -0.25)$, and crosses the y-axis at $(0,6)$. This information can be used to sketch the graph accurately.