What is the vertex of the parabola represented by the equation y = 3x^2 - 12x +

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Question: What is the vertex of the parabola represented by the equation y = 3x^2 - 12x + 7? (2023)

Options:

Correct Answer: (2, -5)

Exam Year: 2023

Solution:

The vertex can be found using x = -b/(2a). Here, x = 12/(2*3) = 2. Substituting x = 2 into the equation gives y = 3(2)^2 - 12(2) + 7 = -5.

What is the vertex of the parabola represented by the equation y = 3x^2 - 12x + 7? (2023)

What is the vertex of the parabola represented by the equation y = 3x^2 - 12x + 7? (2023)

Step 1: Identify the coefficients from the equation y = 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 and a into the formula: x = -(-12)/(2*3).
Step 4: Simplify the expression: x = 12/(6) = 2.
Step 5: Now, substitute x = 2 back into the original equation to find the y-coordinate: y = 3(2)^2 - 12(2) + 7.
Step 6: Calculate y: y = 3(4) - 24 + 7 = 12 - 24 + 7 = -5.
Step 7: The vertex of the parabola is (2, -5).

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