To write the quadratic function f(x) = x² + 8x + 20 in the form f(x) = a(x – h)² + k, we’ll follow a process called completing the square. This technique allows us to express the quadratic in vertex form, making it easier to identify its vertex.

1. **Starting with the equation**: We have the function f(x) = x² + 8x + 20.

2. **Isolate the quadratic and linear terms**: We focus on the terms x² + 8x. To complete the square, we take the coefficient of x, which is 8, halve it (which gives us 4), and square it (4² = 16).

3. **Rewrite the equation**: Add and subtract this square value within the expression. Thus, we rewrite the equation as:

f(x) = (x² + 8x + 16) + 20 – 16

4. **Factoring the perfect square trinomial**: The expression inside the parentheses can be factored:

f(x) = (x + 4)² + 4

5. **Identifying the vertex**: Now that we have our function in vertex form f(x) = a(x – h)² + k, we can identify h and k:

• h = -4 (noting that we have (x + 4), hence x – (-4))
• k = 4

***Vertex of the parabola***: The vertex of the graph of this function is at the point (-4, 4).

In conclusion, the quadratic function in vertex form is f(x) = (x + 4)² + 4, and its vertex is located at (-4, 4).