To find \( k(-3) \), substitute \( x = -3 \) into the function \( k(x) = 4x^2 + 1 \):

\[
k(-3) = 4(-3)^2 + 1
\]

Now, calculate step by step:

\[
k(-3) = 4(9) + 1 = 36 + 1 = 37
\]

Thus, \( k(-3) = 37 \).

Would you like any additional details or further explanations?

Here are some related questions you could explore:
1. What is \( k(2) \) for the same function?
2. How would you find the value of \( k(x) \) for a general value of \( x \)?
3. What is the vertex of the quadratic function \( k(x) = 4x^2 + 1 \)?
4. How would you graph \( k(x) = 4x^2 + 1 \)?
5. What is the derivative of \( k(x) = 4x^2 + 1 \)?

**Tip:** The value of \( x^2 \) is always positive, so quadratic functions of the form \( ax^2 + b \) will always have a minimum point when \( a > 0 \).

Learn how to evaluate the quadratic function k(x) = 4x^2 + 1 by substituting x = -3. This problem involves algebraic concepts, including substitution and quadratic functions, suitable for students in Grades 8-10.

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