Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a

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Question: Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a minimum.

Options:

Correct Answer: 2

Solution:

The vertex occurs at x = -b/(2a) = 4/2 = 2, which is the x-coordinate of the minimum point.

Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a minimum.

Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a minimum.

Correct Answer: 2

Step 1: Identify the function you are working with, which is f(x) = x^2 - 4x + 5.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = 1, b = -4, and c = 5.
Step 3: To find the x-coordinate of the minimum point, use the formula x = -b/(2a).
Step 4: Substitute the values of a and b into the formula: x = -(-4)/(2*1).
Step 5: Simplify the expression: x = 4/2.
Step 6: Calculate the result: x = 2.
Step 7: Conclude that the x-coordinate of the point where the function has a minimum is 2.

Quadratic Functions – Understanding the properties of quadratic functions, including how to find the vertex and minimum value.
Vertex Formula – Using the vertex formula x = -b/(2a) to find the x-coordinate of the vertex of a parabola.