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What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)

Practice Questions

Q1
What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)
  1. -5
  2. -4
  3. -3
  4. -2

Questions & Step-by-Step Solutions

What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)
  • Step 1: Identify the function we are working with, which is f(x) = 3x^2 - 12x + 7.
  • Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = 3, b = -12, and c = 7.
  • Step 3: Find the x-coordinate of the vertex using the formula x = -b / (2a). Here, b = -12 and a = 3.
  • Step 4: Calculate x = -(-12) / (2 * 3) = 12 / 6 = 2.
  • Step 5: Now, substitute x = 2 back into the function to find the minimum value: f(2) = 3(2^2) - 12(2) + 7.
  • Step 6: Calculate f(2) = 3(4) - 24 + 7 = 12 - 24 + 7 = -5.
  • Step 7: Therefore, the minimum value of f(x) is -5.
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