The standard form of a quadratic function is given by:

\[ f(x) = a(x - h)^2 + k \]

where \((h, k)\) is the vertex of the parabola. To convert \( f(x) = x^2 + 8x \) into this form, we complete the square:

1. Start with the given function:
   \[
   f(x) = x^2 + 8x
   \]

2. Add and subtract \(\left( \frac{8}{2} \right)^2 = 16\) inside the function:
   \[
   f(x) = x^2 + 8x + 16 - 16
   \]

3. Rewrite it as a perfect square:
   \[
   f(x) = (x + 4)^2 - 16
   \]

So, the standard form is:

\[
f(x) = (x + 4)^2 - 16
\]

This form shows that the vertex of the parabola is \((-4, -16)\).

Do you want more details or have any questions? Here are 5 related questions:

1. How do you find the vertex of a quadratic function?
2. What is the axis of symmetry for the function \( f(x) = (x + 4)^2 - 16 \)?
3. How do you convert a quadratic function from standard form to general form?
4. Can you explain how to graph \( f(x) = (x + 4)^2 - 16 \)?
5. What are the x-intercepts of the function \( f(x) = x^2 + 8x \)?

**Tip:** Completing the square is a helpful technique for converting a quadratic function into standard form, which makes it easier to identify the vertex and graph the function.

Learn how to convert the quadratic function f(x) = x^2 + 8x into standard form by completing the square. This step-by-step explanation covers key algebra concepts and the completing the square method, ideal for students in Grades 8-10.

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