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For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (202

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Question: For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (2023)

Options:

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

Correct Answer: 2

Exam Year: 2023

Solution: 

The vertex x-coordinate is given by -b/(2a) = -4/(2*-1) = 2.

For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (202

Practice Questions

Q1
For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (2023)
  1. 2
  2. 4
  3. 1
  4. 3

Questions & Step-by-Step Solutions

For the function f(x) = -x^2 + 4x + 1, find the x-coordinate of the vertex. (2023)
  • Step 1: Identify the coefficients a, b, and c from the function f(x) = -x^2 + 4x + 1. Here, a = -1, b = 4, and c = 1.
  • Step 2: Use the formula for the x-coordinate of the vertex, which is -b/(2a).
  • Step 3: Substitute the values of b and a into the formula: -b/(2a) = -4/(2*-1).
  • Step 4: Calculate the denominator: 2 * -1 = -2.
  • Step 5: Now calculate -4 / -2, which equals 2.
  • Step 6: The x-coordinate of the vertex is 2.
  • Quadratic Functions – Understanding the standard form of a quadratic function and how to find the vertex using the formula -b/(2a).
  • Vertex of a Parabola – Identifying the vertex of a parabola represented by a quadratic function and its significance in graphing.
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