For the parabola y = x^2 - 4x + 3, find the coordinates of the vertex.

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Question: For the parabola y = x^2 - 4x + 3, find the coordinates of the vertex.

Options:

Correct Answer: (2, -1)

Solution:

To find the vertex, use x = -b/(2a). Here, a = 1, b = -4, so x = 2. Substitute x = 2 into the equation to find y = -1. Thus, the vertex is (2, -1).

For the parabola y = x^2 - 4x + 3, find the coordinates of the vertex.

For the parabola y = x^2 - 4x + 3, find the coordinates of the vertex.

Step 1: Identify the coefficients a and b from the equation y = x^2 - 4x + 3. Here, a = 1 and b = -4.
Step 2: Use the formula x = -b/(2a) to find the x-coordinate of the vertex. Substitute a and b into the formula: x = -(-4)/(2*1).
Step 3: Calculate the value: x = 4/2 = 2. So, the x-coordinate of the vertex is 2.
Step 4: Substitute x = 2 back into the original equation to find the y-coordinate. Calculate y = (2)^2 - 4*(2) + 3.
Step 5: Simplify the equation: y = 4 - 8 + 3 = -1. So, the y-coordinate of the vertex is -1.
Step 6: Combine the x and y coordinates to find the vertex. The vertex is (2, -1).

Vertex of a Parabola – The vertex of a parabola given in standard form y = ax^2 + bx + c can be found using the formula x = -b/(2a) to determine the x-coordinate, followed by substituting this value back into the equation to find the y-coordinate.