1. The problem is to graph the equation $$y = |x + 3| + 4$$. 2. This is an absolute value function, which creates a V-shaped graph. 3. The general form of an absolute value function is $$y = |x - h| + k$$, where $(h, k)$ is the vertex of the graph. 4. In our equation, $$y = |x + 3| + 4$$, we can rewrite $$x + 3$$ as $$x - (-3)$$, so the vertex is at $$(-3, 4)$$. 5. The graph opens upwards because the coefficient of the absolute value is positive. 6. To plot the graph, start at the vertex $(-3, 4)$. 7. For values of $x$ greater than $-3$, the graph increases linearly with slope 1. 8. For values of $x$ less than $-3$, the graph decreases linearly with slope -1. 9. The graph is symmetric about the vertical line $x = -3$. 10. The y-intercept can be found by substituting $x=0$: $$y = |0 + 3| + 4 = 3 + 4 = 7$$. 11. The x-intercepts can be found by solving $$0 = |x + 3| + 4$$, which has no solution since $$|x + 3| + 4 \geq 4 > 0$$. 12. Therefore, the graph does not cross the x-axis. Final answer: The graph is a V-shaped curve with vertex at $(-3,4)$, opening upwards, y-intercept at $(0,7)$, and no x-intercepts.