What is the vertex of the parabola represented by the equation y = x² - 6x + 8?

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Question: What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)

Options:

Correct Answer: (3, -1)

Solution:

The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.

What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)

What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)

Step 1: Identify the coefficients in the equation y = x² - 6x + 8. Here, a = 1, b = -6, and c = 8.
Step 2: Use the formula to find the x-coordinate of the vertex: x = -b / (2a). Substitute b and a into the formula: x = -(-6) / (2 * 1).
Step 3: Simplify the calculation: x = 6 / 2 = 3.
Step 4: Now, substitute x = 3 back into the original equation to find the y-coordinate: y = (3)² - 6(3) + 8.
Step 5: Calculate y: y = 9 - 18 + 8 = -1.
Step 6: The vertex of the parabola is (3, -1).

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