Understanding Maximum and Minimum Problems with Quadratic Functions

Solving problems to find maximum and minimum values can be tough.

Let’s break it down!

1. Vertex Form: A quadratic function can be written in a special way called vertex form. It looks like this:
   y = a(x - h)² + k
   Here, (h, k) is the vertex. The vertex is the highest or lowest point of the graph.

2. Finding the Vertex: Figuring out the values of h and k can be confusing. It often helps to think about what the problem is asking.

3. Maximum and Minimum: The value of a tells us whether we have a maximum or a minimum.

   • If a is less than 0 (a negative number), the highest point (maximum) is at k.
   • If a is greater than 0 (a positive number), the lowest point (minimum) is at k.

These ideas might take a bit of practice, but once you get the hang of them, you'll be able to solve similar problems much more easily!