Quiz about Unit 6 Assessment 3 Extra Practice

Question 1

Identify the center and radius for the following circle:

(x + 2)² + (y - 7)² = 25

Accepted Answer

Center: (-2, 7)

Radius: r = 5

Answer

Center: (2, -7)

Radius: r = 5

Answer

Center: (-2, 7)

Radius: r = 25

Answer

Center: (2, 7)

Radius: r = 5

Question 2

Identify the center and radius for the following circle:

x² + (y - 1)² = 81

Accepted Answer

Center: (0, 1)

Radius: r = 9

Answer

Center: (0, -1)

Radius: r = 9

Answer

Center: (0, 1)

Radius: r = 81

Answer

Center: (1, 0)

Radius: r = 9

Question 3

Which of the following is the equation for a circle with a center (-4, -5) and a diameter of 12?

Accepted Answer

(x + 4)² + (y + 5)²= 36

Answer

(x + 4)² + (y + 5)² = 144

Answer

(x + 4)² + (y + 5)² = 12

Answer

(x - 4)² + (y - 5)² = 144

Question 4

Which of the following is the equation for a circle with a center (0, 0) and a radius of $$\sqrt[]{3}$$ ?

Accepted Answer

x² + y² = 3

Answer

x²+ y² = $$\sqrt[]{3}$$

Answer

(x - $$\sqrt[]{3}$$ )² + (y - $$\sqrt[]{3}$$ )² = 3

Answer

x² + y²= 9

Question 5

Which of the following is the equation for the circle shown below?

Accepted Answer

(x - 5)² + (y + 5)² = 16

Answer

(x + 5)² + (y + 5)² = 16

Answer

(x - 5)² + (y + 5)²= 25

Answer

(x + 5)² + (y - 5)²= 16

Question 6

A circle is centered at (6, -8). The point (3, 4) is on the circle. Determine which of the following is the equation of the circle.

Accepted Answer

(x - 6)² + (y + 8)²= 5

Answer

(x + 6)² + (y + 8)²= 5

Answer

(x + 6)² + (y - 8)²= 5

Answer

(x - 6)² + (y - 8)²= 5

Question 7

Complete the square: x² + 20x - 27 = 0

Accepted Answer

(x + 10)² = 127

Answer

(x + 10)² = 73

Answer

(x + 100)² = 37

Answer

(x + 20)² = 427

Question 8

A student tried completing the square for the problem below, but made a mistake. In which step is the mistake?

Problem: x² - 8x - 72

STEP 1: x² - 8x = 72

STEP 2: x² - 8x + 16 = 72 + 16

STEP 3: (x + 1)² = 88

Accepted Answer

Step 3

Answer

Step 1

Answer

Step 2

Answer

The student made no mistakes :-)

Question 9

A student tried completing the square for the problem below, but made a mistake. In which step is the mistake and how can you fix it?

Problem: x² + 6x + 8 = 0

STEP 1: x² + 6x = -8

STEP 2: x² + 6x + 6 = -8 + 6

STEP 3: (x + 3)² = -2

Accepted Answer

Step 2:

The student should be adding 9 on both sides, not 6.

Answer

Step 1:

The right side of the equation should be positive 8.

Answer

Step 2:

The student should be subtracting 6 on both sides, not adding 6.

Answer

Step 3:

Inside the parenthesis should be (x - 3)

Answer

Step 2:

The student should be adding 3 on both sides, not 6.

Question 10

Given the equation: x² + 8x + y² - 2y = 64, which of the following correctly fills in the blank of the steps of solving by completing the square?

x² + 8x + y² - 2y = 64

x² + 8x + A + y² - 2y + B = 64 + A + B

Accepted Answer

A = 16

B = 1

Answer

A = 16

B = 4

Answer

A = 64

B = 2

Answer

A = 64

B = -1

Question 11

Given the equation: x² - 4x + y² + 10y - 7 = 0, which of the following correctly fills in the numbers in the last step?

x² - 4x + y² + 10y - 7 = 0

x² - 4x + y² + 10y = 7

x² - 4x + 4 + y² + 10y + 25 = 7 + 4 + 25

(x + A)² + (y + B)² = 36

Accepted Answer

A = -2

B = 5

Answer

A = 4

B = 25

Answer

A = 2

B = 10

Answer

A = -4

B = -5

Question 12

Identify the center and radius of the circle represented by the equation

x² + 14x + y² - 12y + 4 = 0

(HINT: Write the equation in standard form by completing the square.)

Accepted Answer

Center: (-7, 6)

Radius: r=9

Answer

Center: (-7, -6)

Radius: r=85

Answer

Center: (7, -6)

Radius: r=85

Answer

Center: (7, 6)

Radius: r=9

Unit 6 Assessment 3 Extra Practice

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