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

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

Options:

Correct Answer: (2, 0)

Solution:

The vertex can be found using the formula x = -b/(2a). Here, a = 1, b = -4, so x = 2. Substitute x back to find y: y = 0.

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

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

Step 1: Identify the coefficients in the equation y = x^2 - 4x + 4. Here, a = 1 and b = -4.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a).
Step 3: Substitute the values of a and b into the formula: x = -(-4)/(2*1).
Step 4: Simplify the equation: x = 4/2 = 2.
Step 5: Now that we have x = 2, substitute this value back into the original equation to find y: y = (2)^2 - 4*(2) + 4.
Step 6: Calculate y: y = 4 - 8 + 4 = 0.
Step 7: The vertex of the parabola is (2, 0).

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