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.

Because it is warm outside I'm growing some plants in my backyard.  For me planting vegetables is similar to a math problem.  Let's say if I want to grow a watermelon in my yard, there are different ways to start. One way is to start by letting the seed sprout in the house.  This means that you will have to start one or two weeks prior to the day you want to plant the plant outside.  But this also means that you will know your plant is growing and it will take a shorter time to mature, than just planting it in the ground.   But if you plant the seeds outside you would just need to water them every 2-3 days.  This means that you won't have as much responsibility.  For me, I would choose the first way to plant the seed.  This is because there's a more possible chance of the plant growing.  This is like a quadratic equation because there can be many ways to get to an answer, but there are ways that are more likely able to get you to the right answer.  

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