Understanding Completing the Square and Circle Equations

The video tutorial covers the process of completing the square for both x and y variables to form perfect square trinomials. The instructor uses color coding to enhance understanding and demonstrates how to balance equations by adding terms to both sides. The lesson concludes with factoring the trinomials and identifying the center and radius of a circle from the equation.

Why does the teacher choose Christmas colors for the color coding?

• Because it is easier to see

• Because it is a school tradition

• Because it reminds them of winter

• Because it is December

What is the first step in solving the problem?

• Factoring the equation

• Finding the radius

• Completing the square for Y

• Grouping the variables

What value do you get when you complete the square for the X variable?

• 4

• 8

• 16

• 2

What is the value of B/2 for the Y variable?

• 4

• 2

• 8

• 16

Where should you add the squared value when completing the square?

• Outside the parentheses

• Inside the parentheses

• On the left side of the equation

• On the right side of the equation

What must you do after adding the squared value inside the parentheses?

• Subtract it from the other side

• Multiply it by 2

• Add it to the other side

• Ignore it

What is the resulting equation after adding the squared values?

• x^2 - 8x + 16 + y^2 + 4y + 4 = 30

• x^2 - 8x + 16 + y^2 + 4y + 4 = 20

• x^2 - 8x + 16 + y^2 + 4y + 4 = 24

• x^2 - 8x + 16 + y^2 + 4y + 4 = 16

What do you get when you factor the equation x^2 - 8x + 16?

• (x + 2)^2

• (x + 4)^2

• (x - 4)^2

• (x - 2)^2

What is the center of the circle in the final equation?

• (-4, 2)

• (4, -2)

• (4, 2)

• (-4, -2)

What is the radius of the circle in the final equation?

• 4

• 2

• 3

• 5