Math Problem Statement

k(x) 4x^2+1 k(-3)=

Solution

To find k(3)k(-3), substitute x=3x = -3 into the function k(x)=4x2+1k(x) = 4x^2 + 1:

k(3)=4(3)2+1k(-3) = 4(-3)^2 + 1

Now, calculate step by step:

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

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

Would you like any additional details or further explanations?

Here are some related questions you could explore:

  1. What is k(2)k(2) for the same function?
  2. How would you find the value of k(x)k(x) for a general value of xx?
  3. What is the vertex of the quadratic function k(x)=4x2+1k(x) = 4x^2 + 1?
  4. How would you graph k(x)=4x2+1k(x) = 4x^2 + 1?
  5. What is the derivative of k(x)=4x2+1k(x) = 4x^2 + 1?

Tip: The value of x2x^2 is always positive, so quadratic functions of the form ax2+bax^2 + b will always have a minimum point when a>0a > 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Substitution

Formulas

k(x) = 4x^2 + 1

Theorems

Quadratic Function Properties

Suitable Grade Level

Grades 8-10