To determine which graph corresponds to the quadratic function $y = x^2 + 10x + 16$, we need to analyze the function's properties.

First, we find the vertex of the parabola. The vertex form of a quadratic function $y = ax^2 + bx + c$ has its vertex at $(h, k)$ where $h = -\frac{b}{2a}$.

For $y = x^2 + 10x + 16$:

$a = 1, \quad b = 10$

So,

$h = -\frac{10}{2 \cdot 1} = -5$

Next, we calculate the y-coordinate of the vertex by substituting $x = -5$ back into the function:

$k = (-5)^2 + 10(-5) + 16 = 25 - 50 + 16 = -9$

Thus, the vertex of the parabola is $(-5, -9)$.

Next, we check the y-intercept of the function, which is the constant term $c = 16$. This means the graph will cross the y-axis at $y = 16$.

Now, we analyze the given graphs:

• Graph A: Vertex is not at $(-5, -9)$.
• Graph B: Vertex is at $(-5, -9)$ and the y-intercept is $16$.
• Graph C: Vertex is not at $(-5, -9)$.
• Graph D: Vertex is not at $(-5, -9)$.

Graph B is the only graph that correctly shows the vertex at $(-5, -9)$ and the y-intercept at $16$.

Therefore, the answer is:

$\boxed{\text{B. Graph B}}$

Do you want details or have any questions? Here are five more questions you might ask:

1. How do you determine the vertex of a quadratic function?
2. What are the key features to look for when graphing a quadratic function?
3. How do you find the axis of symmetry of a parabola?
4. How can you find the roots of a quadratic function using the quadratic formula?
5. What is the significance of the discriminant in a quadratic equation?

Tip: When analyzing the graph of a quadratic function, always identify the vertex and y-intercept to confirm its correct placement on the coordinate plane.