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For the function f(x) = 3x^2 - 12x + 7, find the minimum value. (2022)
For the function f(x) = 3x^2 - 12x + 7, find the minimum value. (2022)
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Q1
For the function f(x) = 3x^2 - 12x + 7, find the minimum value. (2022)
-5
-4
-3
-2
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The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 7 = -5.
Questions & Step-by-step Solutions
1 item
Q
Q: For the function f(x) = 3x^2 - 12x + 7, find the minimum value. (2022)
Solution:
The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 7 = -5.
Steps: 7
Show Steps
Step 1: Identify the function you 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: To find the minimum value, calculate the x-coordinate of the vertex using the formula x = -b/(2a).
Step 4: Substitute the values of a and b into the formula: x = -(-12)/(2*3) = 12/6 = 2.
Step 5: Now that we have x = 2, substitute this value back into the function to find the minimum value: f(2) = 3(2^2) - 12(2) + 7.
Step 6: Calculate f(2): f(2) = 3(4) - 24 + 7 = 12 - 24 + 7 = -5.
Step 7: The minimum value of the function f(x) is -5.
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