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What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?

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Question: What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?

Options:

  1. -1
  2. -2
  3. -3
  4. -4

Correct Answer: -2

Solution: 

The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.

What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?

Practice Questions

Q1
What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
  1. -1
  2. -2
  3. -3
  4. -4

Questions & Step-by-Step Solutions

What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
Correct Answer: -2
  • Step 1: Identify the function f(x) = kx^2 + 2x + 1.
  • Step 2: Recognize that this is a quadratic function, which has a minimum value when x = -b/(2a).
  • Step 3: In the function, a = k and b = 2. So, the x value for the minimum is x = -2/(2k).
  • Step 4: Substitute x = -2/(2k) into the function f(x) to find the minimum value.
  • Step 5: Set the minimum value equal to -3, since we want the minimum value to be -3.
  • Step 6: Solve the equation f(-2/(2k)) = -3 for k.
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