Quadratic Equations: Like driving a car

A response to the Like Driving a Car Activity
created by Alexandra Hudyma (@akhudyma)

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After successfully completing the typical high-school unit on quadratic equations, students may jump into the process of solving a quadratic equation automatically and without having to think about it. However, the steps are made up of so many smaller components, each one requiring its own understanding. 

To solve a quadratic equation (in particular, a quadratic equation written in standard form), you must complete the following steps – each of which requires its own set of knowledge and skills:

  1. Recognize that the equation is a quadratic, and that it is written in standard form.
  2. Factor the equation. This involves:
    • Determining which method(s) to use to factor the equation. This requires knowledge of what the different possible factoring methods are, and when they should be applied.
    • Correctly executing the factoring of the equation. This requires a thorough understanding of factors/multiples, as well as the basic arithmetic operations multiplication, addition, subtraction, and potentially division.
    • Knowing when to stop, i.e. when the equation has been fully factored.
  3. Use the zero-product property to solve the equation. This involves:
    • Understanding what the zero-product property is and how you can apply it to a factored equation
    • Being able to solve linear equations for an unknown variable (this again takes knowledge of balancing equations, and basic arithmetic operations).
  4. Write the solutions of the equation. For this, you need to know:
    • What a solution to an equation in one variable is
    • How you obtain the solution from solving a linear equation
    • Recognizing when there are no real solutions, and when two solutions are the same one

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