Solving quadratic equations is one of the main topics of this unit. some quadratic equations can be solved with only one method, some can be solved with multiple methods, and some can’t be solved at all. think about a task in your daily life that can be accomplished in a variety of ways. how do you decide the best course of action for accomplishing that task? how is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?

We use methods in everyday life. In fact, we took many decisions getting a conclusion from the method we use in a topic. 

Think about a task in your daily life that can be accomplished in a variety of ways.

Thinking about a task in our everyday life we can give an example of choosing food in a restaurant. There's a variety of options to be taken and we need to decide what kind of food we are going to eat. What are the methods? I think there's several of them, I will mention three:

Method 1. We have eaten several times in this place and we love a specific type of food, so we choose to eat it again. 

Method 2. Someone tells us that a specific type of food is delicious.

Method 3. The waitress recommends us a specific type of food.

How do you decide the best course of action for accomplishing that task?

Applying any of the methods above we can choose the type of food we would eat. So, we have taken a decision based on our confidence of the method so, the conclusion is that the waitress will serve a specific type of food, but it doesn't mean that we would like this food. It would be possible that we would not like what we are eating, but we choose a specific method for this purpose based maybe on what we know which will work better.

How is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?

The same happens with the method we chose for solving a quadratic equation. Maybe one method can work for a specific type of equation but it does not mean that this one must work for others type of them. So, the way I choose for solving the equation will determine the result or conclusion I get for it. Maybe I return to the restaurant next week and ask for another type of food and never eat the food I didn't like. Applying this to our mathematical problem, maybe I never choose a specific method for a specific quadratic equation.