Understanding the process for solving quadratic equations

The  exercise appears under the Algebra I Math Mission. This exercise explores the process of solving quadratic equations via the Square Root Property.

Types of Problems
There are three types of problems in this exercise:


 * 1) Put the steps of the process in order: This problem provides a quadratic equation that is written in a "vertex" form. The student is asked to select the correct steps that can be used to solve the equation and drag them in order to the space provided.Utpfsqe1.png
 * 2) Fill in the missing step: This problem has a worked out solution to a quadratic equation that is missing one line. The student is asked to select the correct missing step to complete the solution process.Utpfsqe2.png
 * 3) Find the step where an error occurs: This problem has an incorrectly worked out solution to a quadratic equation. The student is asked to select the step in which the error occurs.Utpfsqe3.png

Strategies
Knowledge of the Square Root Property would ensure success on this exercise, but it can be picked up practicing on examples.
 * 1) The Square Root Property says that the solutions to $$x^2=a^2$$ are $$x=+-a$$.
 * 2) The process on the first problem type seems to have four steps consistently, 1) add/subtract, 2) multiply/divide, 3) take a square root, and 4) add/subtract to isolate x.
 * 3) Some errors that occur on the third problem type are leaving out "plus/minus" when taking a square root, or performing opposite operations from what is needed, for example, subtracting when addition is required.

Real-life Applications

 * 1) Quadratics are used to model gravity in physics.
 * 2) Quadratics can be used to model cost function in business applications.