For the function f(x) = x^2 - 6x + 10, what is the minimum value? (2020)

For the function f(x) = x^2 - 6x + 10, what is the minimum value? (2020)

Step 1: Identify the function given, which is f(x) = x^2 - 6x + 10.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c.
Step 3: Find the x-coordinate of the vertex using the formula x = -b/(2a). Here, a = 1 and b = -6.
Step 4: Calculate the x-coordinate of the vertex: x = -(-6)/(2*1) = 6/2 = 3.
Step 5: Now, substitute x = 3 back into the function to find the minimum value: f(3) = 3^2 - 6*3 + 10.
Step 6: Calculate f(3): f(3) = 9 - 18 + 10 = 1.
Step 7: Conclude that the minimum value of the function is 1.

Quadratic Functions – Understanding the properties of quadratic functions, including how to find the vertex and minimum/maximum values.
Vertex Formula – Using the vertex formula x = -b/(2a) to find the x-coordinate of the vertex for a quadratic function.
Function Evaluation – Evaluating the function at the vertex to determine the minimum or maximum value.