Perfect Square Trinomials and Completing the Square

The video tutorial explains how to determine the constant term needed to make an expression a perfect square trinomial. This skill is essential for solving quadratic equations using the method of completing the square. The tutorial provides three examples with different values of B, demonstrating the process of finding the constant term and verifying it by factoring the trinomial into two equal factors. The video emphasizes that the constant term in a perfect square trinomial is always positive.

What is the purpose of making an expression a perfect square trinomial?

• To make the expression linear

• To solve quadratic equations using completing the square

• To simplify the expression

• To eliminate the middle term

Tags

CCSS.HSA-REI.B.4B

If B = 8, what is the constant term that should be added to make the expression a perfect square trinomial?

• 64

• 8

• 16

• 4

Tags

CCSS.HSA.APR.C.4

What are the factors of the trinomial when B = 8 and the constant term is added?

• (x + 8)(x + 8)

• (x + 2)(x + 2)

• (x + 16)(x + 16)

• (x + 4)(x + 4)

Tags

CCSS.HSA-REI.B.4B

For B = -14, what is the constant term that makes the expression a perfect square trinomial?

• 14

• 28

• 49

• -14

Tags

CCSS.HSA.APR.C.4

What are the factors of the trinomial when B = -14 and the constant term is added?

• (x - 7)(x - 7)

• (x - 14)(x - 14)

• (x + 14)(x + 14)

• (x + 7)(x + 7)

Tags

CCSS.HSA.APR.C.4

Why is the constant term always positive in a perfect square trinomial?

• Because a negative constant term cannot form a perfect square

• Because it eliminates the middle term

• Because it makes the expression linear

• Because it simplifies the expression

Tags

CCSS.HSA-REI.B.4B

When B = -7, what is the constant term that should be added to make the expression a perfect square trinomial?

• 14

• 49

• 49/4

• 7/2

Tags

CCSS.HSA.APR.C.4

What is the expression for the perfect square trinomial when B = -7?

• (x + 7)(x + 7)

• (x + 7/2)(x + 7/2)

• (x - 7)(x - 7)

• (x - 7/2)(x - 7/2)

Tags

CCSS.HSA-REI.B.4B

What is the significance of the term B/2 in the context of perfect square trinomials?

• It is the factor of the trinomial

• It is the leading coefficient

• It is the constant term

• It is the term before squaring to get the constant term

In the example with B = -7, why is it more involved than when B is even?

• Because it has a negative constant term

• Because it has a larger constant term

• Because it involves fractions

• Because it requires more calculations