Completing the Square Techniques

The video tutorial explains how to write quadratic expressions in the form of (x + a)^2 + b by creating perfect square trinomials. It provides three examples, each with different coefficients, to demonstrate the process of completing the square. The tutorial covers the addition and subtraction of constants to maintain equality and highlights the importance of factoring into binomial factors. The examples include cases with positive, negative, and odd coefficients, illustrating the method's versatility.

What is the goal when rewriting a quadratic expression in the form of a perfect square trinomial plus a constant?

• To factor the expression

• To simplify the expression

• To isolate the x term

• To create a perfect square trinomial

In the first example, what constant is added to make the expression a perfect square trinomial?

• 4

• 3

• 9

• 6

What is the result of factoring the expression x^2 + 6x + 9?

• (x + 4)^2

• (x + 6)^2

• (x + 9)^2

• (x + 3)^2

In the second example, what is the value of B divided by 2 squared?

• 18

• 36

• 12

• 6

What is the final expression for the second example after completing the square?

• (x - 12)^2 + 36

• (x - 6)^2 + 36

• (x - 12)^2 + 44

• (x - 6)^2 + 44

In the third example, what is the value of B divided by 2?

• -10

• -2.5

• -5/2

• -5

What constant is added to the expression in the third example to make it a perfect square trinomial?

• 12/4

• 37/4

• 5/2

• 25/4

What is the final expression for the third example after completing the square?

• (x - 5)^2 - 25/4

• (x - 5/2)^2 - 25/4

• (x - 5)^2 - 37/4

• (x - 5/2)^2 - 37/4

Why is the third example more involved than the previous ones?

• Because it involves fractions

• Because the expression is not factorable

• Because B is odd

• Because B is a larger number

What is the purpose of subtracting the constant added to make a perfect square trinomial?

• To isolate the x term

• To balance the equation

• To simplify the expression

• To factor the expression