Find the minimum value of the function f(x) = x^2 - 4x + 5.
Practice Questions
Q1
Find the minimum value of the function f(x) = x^2 - 4x + 5.
1
2
3
4
Questions & Step-by-Step Solutions
Find the minimum value of the function f(x) = x^2 - 4x + 5.
Step 1: Identify the function you need to analyze, which is f(x) = x^2 - 4x + 5.
Step 2: Recognize that this function is a quadratic function, which means it forms a parabola.
Step 3: Determine the formula to find the x-coordinate of the vertex of the parabola, which is x = -b/(2a). Here, a = 1 and b = -4.
Step 4: Plug in the values of a and b into the formula: x = -(-4)/(2*1) = 4/2 = 2.
Step 5: Now that you have the x-coordinate of the vertex (x = 2), substitute this value back into the function to find the minimum value: f(2) = 2^2 - 4(2) + 5.
Step 6: Calculate f(2): f(2) = 4 - 8 + 5 = 1.
Step 7: Conclude that the minimum value of the function f(x) is 1.
Quadratic Functions – Understanding the properties of quadratic functions, including their vertex and minimum/maximum values.
Vertex Formula – Using the vertex formula x = -b/(2a) to find the x-coordinate of the vertex of a parabola.
Function Evaluation – Evaluating the function at the vertex to find the minimum or maximum value.
