Transforming Quadratic Equations by Completing the Square

This video tutorial teaches how to transform quadratic equations by completing the square. It begins with an introduction to the concept, followed by a review of perfect square trinomials and their patterns. The video highlights common mistakes, such as failing to preserve equality when solving equations. A detailed example problem is presented, demonstrating the step-by-step process of completing the square. The tutorial concludes with a verification of the transformation, ensuring the equation remains unchanged, and a summary of the lesson.

What is the relationship between the B term and the last term in a perfect square trinomial?

• The last term is half the B term.

• The B term is the square of the last term.

• The last term is the square of half the B term.

• The B term is double the last term.

What is a common mistake students make when completing the square?

• Adding the same number to both sides.

• Not preserving the equality of the equation.

• Using the wrong formula for factoring.

• Forgetting to factor the trinomial.

Why is it important to add the same number to both sides of an equation?

• To simplify the equation.

• To factor the equation correctly.

• To make the equation easier to solve.

• To ensure the equation remains balanced.

In the example provided, what was the first step to transform the quadratic equation?

• Divide both sides by 2.

• Add 5 to both sides.

• Subtract 5 from both sides.

• Multiply both sides by 2.

What does the graph comparison at the end of the example demonstrate?

• The transformation was incorrect.

• The transformation changed the equation.

• The equations are equivalent.

• The equations are different.