Exploring the Basics of Completing the Square

What is the main goal of the video?

• To learn how to solve linear equations

• To understand the process of completing the square

• To explore the properties of circles

• To study the Pythagorean theorem

What is a perfect square trinomial?

• A specific type of trinomial where the two factors are the same

• A trinomial that cannot be factored

• A trinomial with no real roots

• A trinomial where the two factors are different

In the example given, what are the two factors of 9 that add up to 6?

• 2 and 4

• 1 and 9

• 4 and 5

• 3 and 3

What happens to the equation if you add and subtract the same number?

• The equation becomes unsolvable

• The equation changes

• The equation remains the same

• The equation becomes a linear equation

Why do we add and subtract the same number when completing the square?

• To simplify the equation

• To ensure the equation remains unchanged

• To make the equation more complex

• To change the equation

What is the next step after identifying the number to add and subtract?

• Divide the equation by that number

• Multiply the equation by that number

• Factor the perfect square trinomial

• Solve for x

In the example y = x^2 + 8x - 2, what number do we add and subtract?

• 8

• 4

• 2

• 16

What is the vertex form of the equation y = x^2 + 8x - 2 after completing the square?

• y = (x + 4)^2 - 18

• y = (x - 4)^2 + 18

• y = (x + 4)^2 + 18

• y = (x - 4)^2 - 18

What is the result of expanding and simplifying (x + 4)^2 - 18?

• x^2 + 8x - 2

• x^2 + 8x + 16 - 18

• x^2 + 4x + 4x + 16 - 18

• All of the above

What is the final vertex form of the equation y = x^2 - 10x + 18?

• y = (x - 5)^2 + 7

• y = (x + 5)^2 + 7

• y = (x - 5)^2 - 7

• y = (x + 5)^2 - 7