Completing the square with fractions to find the vertex

The video tutorial explains the process of factoring and creating perfect square trinomials. It begins with an introduction to the concept of perfect square trinomials and the importance of recognizing patterns. The teacher demonstrates how to create a perfect square trinomial by squaring the middle term and adjusting the equation. The tutorial also covers simplifying fractions and emphasizes the importance of understanding patterns in mathematics. The session concludes with practice problems to reinforce the concepts learned.

What is the first step in determining if an expression is a perfect square trinomial?

• Check if the middle term is twice the product of the square roots of the first and last terms.

• Make sure the expression has three terms.

• Ensure all terms are positive.

• Verify that the expression is a binomial.

When creating a perfect square trinomial, what do you do with the middle term?

• Take half of it and square it.

• Multiply it by the last term.

• Double it and add to the expression.

• Subtract it from the first term.

Why is the expression always factorable when completing the square?

• Because it eliminates the middle term.

• Because it involves only whole numbers.

• Because the process ensures a perfect square trinomial is formed.

• Because it uses a specific formula.

What is the relationship between the terms in a perfect square trinomial?

• The last term is the sum of the first and middle terms.

• The middle term is the square of the first term.

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

• The middle term is twice the product of the square roots of the first and last terms.

How can you simplify the expression 1 in terms of fractions?

• Rewrite it as 2/2.

• Rewrite it as 3/3.

• Rewrite it as 4/4.

• Rewrite it as 5/5.