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What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?

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Question: What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?

Options:

  1. 5
  2. 6
  3. 7
  4. 8

Correct Answer: 5

Solution: 

The vertex form gives the maximum value at x = 2, f(2) = 5.

What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?

Practice Questions

Q1
What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?
  1. 5
  2. 6
  3. 7
  4. 8

Questions & Step-by-Step Solutions

What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?
Correct Answer: 5
  • Step 1: Identify the quadratic function, which is f(x) = -x^2 + 4x + 1.
  • Step 2: Recognize that this is a downward-opening parabola because the coefficient of x^2 is negative (-1).
  • Step 3: Find the x-coordinate of the vertex using the formula x = -b/(2a), where a = -1 and b = 4.
  • Step 4: Calculate x = -4/(2 * -1) = -4/-2 = 2.
  • Step 5: Substitute x = 2 back into the function to find the maximum value: f(2) = -2^2 + 4*2 + 1.
  • Step 6: Calculate f(2) = -4 + 8 + 1 = 5.
  • Step 7: Conclude that the maximum value of the function is 5.
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