Find the zeros of each given function: f(x) = x^2 - 8x + 16

To find the zeros of the function \( f(x) = x^2 - 8x + 16 \), we set \( f(x) = 0 \) and solve for \( x \):

\[
x^2 - 8x + 16 = 0
\]

This quadratic can be factored as follows:

\[
(x - 4)(x - 4) = 0
\]

or equivalently,

\[
(x - 4)^2 = 0
\]

To find the solutions, we set \( x - 4 = 0 \):

\[
x = 4
\]

Thus, the only zero of \( f(x) = x^2 - 8x + 16 \) is:

\[
x = 4
\]

This is a repeated root, meaning \( x = 4 \) is a solution with multiplicity 2.

Would you like more details or have any questions?

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Here are some related questions that expand on this topic:

1. What is the geometric interpretation of a repeated root for a quadratic function?
2. How would you find the vertex of the function \( f(x) = x^2 - 8x + 16 \)?
3. How would the zeros change if the function were \( f(x) = x^2 - 8x + 15 \)?
4. Can we use the quadratic formula to verify the result, and how?
5. How can we complete the square to confirm the form \( (x - 4)^2 \)?

**Tip:** For any quadratic equation of the form \( ax^2 + bx + c = 0 \), if the discriminant \( b^2 - 4ac = 0 \), the quadratic has a repeated root.

Learn how to find the zeros of the quadratic function f(x) = x^2 - 8x + 16 with a detailed step-by-step solution. This problem covers algebraic concepts, including factoring and repeated roots, and is suitable for students in Grades 7-9.

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