Given f(x) = x^2 − 2x + 5, find the following.

1. f(−2) =

To solve for \( f(-2) \) when \( f(x) = x^2 - 2x + 5 \), we simply substitute \( x = -2 \) into the function:

\[
f(-2) = (-2)^2 - 2(-2) + 5
\]

Step-by-step:

1. \( (-2)^2 = 4 \)
2. \( -2(-2) = 4 \)
3. So, \( f(-2) = 4 + 4 + 5 = 13 \)

Thus, \( f(-2) = 13 \).

Would you like more details or have any questions? Here are 5 related questions:

1. What is the vertex of the function \( f(x) = x^2 - 2x + 5 \)?
2. How do you find the axis of symmetry for a quadratic function?
3. What is the minimum value of the function \( f(x) = x^2 - 2x + 5 \)?
4. How does completing the square help in analyzing quadratic functions?
5. How would you graph \( f(x) = x^2 - 2x + 5 \)?

**Tip:** When evaluating functions at specific points, always substitute carefully and simplify each term step-by-step to avoid errors.

Learn how to evaluate the quadratic function f(x) = x^2 - 2x + 5 at x = -2 step-by-step. Understand the application of the quadratic formula and solve for f(-2). Suitable for high school students.

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