Determine the maximum value of the function f(x) = -x^2 + 6x - 8. (2022)

Determine the maximum value of the function f(x) = -x^2 + 6x - 8. (2022)

Step 1: Identify the function you want to analyze, which is f(x) = -x^2 + 6x - 8.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = -1, b = 6, and c = -8.
Step 3: Determine the x-coordinate of the vertex using the formula x = -b/(2a). Here, b = 6 and a = -1.
Step 4: Substitute the values into the formula: x = -6/(2*(-1)) = -6/-2 = 3.
Step 5: Now, find the maximum value of the function by substituting x = 3 back into the function f(x).
Step 6: Calculate f(3): f(3) = -3^2 + 6*3 - 8.
Step 7: Simplify the calculation: f(3) = -9 + 18 - 8 = 1.
Step 8: Conclude that the maximum value of the function f(x) is 1.

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