Completing the Square in Quadratic Expressions

Mr. Boyd's lesson focuses on teaching how to complete the square for quadratic expressions. The video begins with an introduction to the learning goals, followed by an explanation of perfect square trinomials and their binomial factors. Key observations are made about the relationship between the terms in the trinomial and binomial. The lesson outlines steps to complete the square, including taking half of the B term, squaring it, and adding it to the expression. Several examples are provided to illustrate the process. The lesson concludes with a call to action to subscribe for more algebra content.

What is the primary purpose of learning to complete the square in algebra?

• To simplify polynomial expressions

• To solve quadratic equations

• To graph linear equations

• To factorize prime numbers

What does a perfect square trinomial result from?

• A binomial squared

• A binomial raised to the third power

• A monomial doubled

• A trinomial squared

What is the first step in completing the square for a quadratic expression?

• Add the constant term to x

• Multiply the coefficient of x by 2

• Divide the coefficient of x by 2

• Square the constant term

In the expression x^2 + 6x, what do you add to complete the square?

• 9

• 36

• 12

• 6

What is the factored form of x^2 + 12x + 36?

• (x - 12)^2

• (x - 6)^2

• (x + 12)^2

• (x + 6)^2

For the expression y^2 + 14y, what is the correct completion to make it a perfect square trinomial?

• y + 49

• y + 7

• 7

• 49

What is the factored form of y^2 + 14y + 49?

• (y + 7)^2

• (y - 7)^2

• (y + 49)^2

• (y - 49)^2

If you have y^2 - 10y, what term completes the square?

• -5

• 25

• 5

• -25

What is the factored form of x^2 - 16x + 64?

• (x + 16)^2

• (x - 8)^2

• (x - 16)^2

• (x + 8)^2

What does the sign of the middle term in a quadratic expression influence in the factored form?

• The coefficient of x

• The sign in the binomial factor

• The sign of the constant term

• The exponent on x