Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a
Practice Questions
Q1
Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a local minimum.
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Questions & Step-by-Step Solutions
Find the x-coordinate of the point where the function f(x) = x^2 - 4x + 5 has a local minimum.
Correct Answer: 2
Step 1: Identify the function f(x) = x^2 - 4x + 5.
Step 2: Recognize that this is a quadratic function in the form f(x) = ax^2 + bx + c, where a = 1, b = -4, and c = 5.
Step 3: Use the formula for the x-coordinate of the vertex of a parabola, which is 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 local minimum occurs at x = 2.
Quadratic Functions – Understanding the properties of quadratic functions, including how to find the vertex, which indicates the location of local minima or maxima.
Vertex Formula – Using the vertex formula x = -b/(2a) to find the x-coordinate of the vertex of a parabola represented by a quadratic function.
