AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Determine the minimum value of
Full solution
Q. Determine the minimum value of
- Recognize Quadratic Function: To find the minimum value of the function , we need to recognize that this is a quadratic function in the form of , where is the vertex of the parabola. Since is positive (), the parabola opens upwards, and the vertex represents the minimum point of the function.
- Find Vertex Coordinates: The vertex of the parabola is given by the point . In the function , and , because the function can be rewritten as . Therefore, the vertex is at the point .
- Determine Minimum Value: Since the vertex represents the lowest point on the graph of the function , the minimum value of is the -coordinate of the vertex. Therefore, the minimum value of is .
