What is the vertex of the quadratic equation y = x^2 - 4x + 3?

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Question: What is the vertex of the quadratic equation y = x^2 - 4x + 3?

Options:

Correct Answer: (2, -1)

Solution:

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

What is the vertex of the quadratic equation y = x^2 - 4x + 3?

What is the vertex of the quadratic equation y = x^2 - 4x + 3?

Step 1: Identify the coefficients a, b, and c from the equation y = x^2 - 4x + 3. Here, a = 1, b = -4, and c = 3.
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) + 3.
Step 4: Simplify the equation: y = 4 - 8 + 3 = -1.
Step 5: Combine the x and y coordinates to find the vertex. The vertex is (2, -1).

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