Calculating Constant Terms in Quadratics

The video tutorial explains how to complete the square for trinomials with a leading coefficient of one. It covers the formula for finding the constant term to make a trinomial a perfect square and provides two examples: one with a positive coefficient and another with a negative coefficient. The tutorial demonstrates the process of factoring the trinomial into binomial factors and verifies the results. Key concepts include understanding the role of the coefficient and constant term in forming a perfect square trinomial.

What is the form of a perfect square trinomial with a leading coefficient of one?

• A trinomial where the constant term is the square of half the linear coefficient.

• A trinomial where the constant term is twice the linear coefficient.

• A trinomial where the constant term is half the linear coefficient.

• A trinomial where the constant term is the square of the linear coefficient.

In the first example, what is the value of B when the coefficient of x is 3?

• B = 6

• B = 1.5

• B = 3

• B = 4.5

How is the value of C calculated when B is a fraction in the first example?

• By subtracting 2 from B and squaring the result.

• By dividing B by 2 and squaring the result.

• By adding 2 to B and squaring the result.

• By multiplying B by 2 and squaring the result.

What is the constant term C in the first example after completing the square?

• C = 34

• C = 3/4

• C = 9/16

• C = 916

What is the factorization of the trinomial in the first example?

• (x + 916)^2

• (x + 3/4)^2

• (x + 9/16)^2

• (x + 34)^2

In the second example, what is the value of B when the coefficient of x is -4?

• B = -4

• B = -2

• B = -8

• B = -16

How is the value of C calculated in the second example?

• By squaring B and multiplying by 12.

• By dividing B by 2 and squaring the result.

• By multiplying B by 2 and squaring the result.

• By squaring B and dividing by 2.

What is the constant term C in the second example after completing the square?

• C = 25

• C = 4/25

• C = 425

• C = 4

What is the factorization of the trinomial in the second example?

• (x - 2/5)^2

• (x - 4/5)^2

• (x - 25)^2

• (x - 425)^2

What were the values that completed the square in the two examples?

• 916 and 4/25

• 34 and 25

• 3/4 and 2/5

• 9/16 and 4/5