For the function f(x) = x^2 - 4x + 5, find the vertex.

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Question: For the function f(x) = x^2 - 4x + 5, find the vertex.

Options:

Correct Answer: (2, 1)

Solution:

The vertex is at x = -b/(2a) = 4/2 = 2. f(2) = 2^2 - 4(2) + 5 = 1, so the vertex is (2, 1).

For the function f(x) = x^2 - 4x + 5, find the vertex.

For the function f(x) = x^2 - 4x + 5, find the vertex.

Correct Answer: (2, 1)

Step 1: Identify the coefficients a, b, and c from the function f(x) = x^2 - 4x + 5. Here, a = 1, b = -4, and c = 5.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a). Substitute the values of b and a: x = -(-4)/(2*1).
Step 3: Simplify the expression: x = 4/2 = 2. This gives us the x-coordinate of the vertex.
Step 4: Now, find the y-coordinate of the vertex by substituting x = 2 back into the function f(x). Calculate f(2) = 2^2 - 4(2) + 5.
Step 5: Simplify f(2): f(2) = 4 - 8 + 5 = 1. This gives us the y-coordinate of the vertex.
Step 6: Combine the x and y coordinates to find the vertex. The vertex is (2, 1).

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