To find the biggest or smallest values in word problems with quadratic equations, follow these simple steps:

1. Standard Form: Change the quadratic equation to the form $y = ax^2 + bx + c$.

   • If $a$ is less than 0, the graph opens downwards, meaning there’s a maximum value.
   • If $a$ is greater than 0, the graph opens upwards, which means there’s a minimum value.

2. Vertex Formula: You can find the vertex, or the tip of the U-shaped graph, using the formula $h = -\frac{b}{2a}$.

   • Then, put this value of $h$ back into the equation to find $k$.
   • Together, $(h, k)$ gives you the coordinates for the maximum or minimum.

3. Graphing: Draw the graph of the quadratic equation.

   • This will help you see where the vertex is located and confirm if you have a maximum or minimum value.

4. Real-life Context: Think about how this problem relates to real life.

   • For example, consider how a thrown ball moves in the air.
   • This can help you understand the maximum or minimum values better.