What is the vertex of the parabola represented by the equation y = x^2 - 4x + 1?

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Question: What is the vertex of the parabola represented by the equation y = x^2 - 4x + 1?

Options:

Correct Answer: (2, -3)

Solution:

Use the vertex formula x = -b/2a: x = 4/2 = 2. Substitute x back to find y: y = 2^2 - 4(2) + 1 = -3. Vertex is (2, -3).

What is the vertex of the parabola represented by the equation y = x^2 - 4x + 1?

What is the vertex of the parabola represented by the equation y = x^2 - 4x + 1?

Step 1: Identify the coefficients a, b, and c from the equation y = x^2 - 4x + 1. Here, a = 1, b = -4, and c = 1.
Step 2: Use the vertex formula x = -b / (2a) to find the x-coordinate of the vertex. Substitute b and a: x = -(-4) / (2 * 1) = 4 / 2 = 2.
Step 3: Substitute the x value back into the original equation to find the y-coordinate. Calculate y = (2)^2 - 4(2) + 1.
Step 4: Simplify the equation: y = 4 - 8 + 1 = -3.
Step 5: Combine the x and y coordinates to find the vertex. The vertex is (2, -3).

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