For the function f(x) = 3x^2 - 12x + 7, find the x-coordinate of the vertex. (20

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Question: For the function f(x) = 3x^2 - 12x + 7, find the x-coordinate of the vertex. (2022)

Options:

Correct Answer: 2

Exam Year: 2022

Solution:

The x-coordinate of the vertex is given by x = -b/(2a) = 12/(2*3) = 2.

For the function f(x) = 3x^2 - 12x + 7, find the x-coordinate of the vertex. (2022)

For the function f(x) = 3x^2 - 12x + 7, find the x-coordinate of the vertex. (2022)

Step 1: Identify the coefficients a, b, and c from the function f(x) = 3x^2 - 12x + 7. Here, a = 3, b = -12, and c = 7.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a).
Step 3: Substitute the value of b into the formula. Since b = -12, we have -(-12) = 12.
Step 4: Calculate 2a. Since a = 3, we have 2 * 3 = 6.
Step 5: Now, divide the result from Step 3 by the result from Step 4. So, x = 12 / 6.
Step 6: Simplify the division. 12 divided by 6 equals 2.
Step 7: Therefore, 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 x = -b/(2a).
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