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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.

Understand how to analyze quadratic functions, focusing on finding the vertex and y-intercept. This problem covers the process of determining the vertex using the vertex form of a quadratic function, identifying key features of graphs, and making comparisons to select the correct graph. Suitable for high school students.

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