What is the vertex of the parabola represented by the equation y = x² - 4x + 3?

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Question: What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)

Options:

Correct Answer: (2, -1)

Solution:

The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.

What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)

What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)

Step 1: Identify the coefficients in the equation y = x² - 4x + 3. Here, a = 1, b = -4, and c = 3.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b / (2a).
Step 3: Substitute the values of b and a into the formula: x = -(-4) / (2 * 1).
Step 4: Simplify the equation: x = 4 / 2 = 2.
Step 5: Now, substitute x = 2 back into the original equation to find the y-coordinate: y = (2)² - 4(2) + 3.
Step 6: Calculate y: y = 4 - 8 + 3 = -1.
Step 7: The vertex of the parabola is (2, -1).

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