Circles in general form: complete the square and graph

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

2. 1.

   Milo rewrites the circle of a pizza and starts with x² + 12x. What number completes the square?

   36
3. 2.

   Noah rewrites the circle of a drum top and starts with x² − 18x. What number completes the square?

   Use the picture in question 1.

   81
5. 3.

   Pia rewrites the circle of a cake and starts with y² + 14y. What number completes the square?

   49
6. 4.

   Ren rewrites the circle of a round flower bed and starts with y² − 8y. What number completes the square?

   Use the picture in question 3.

   16

7. Read this first

   Use this

   The x terms and the y terms each drawn as a square with a missing corner, beside the grid.

8. 5.

   Tala writes the edge of a clock face as x² + y² − 4x + 6y − 12 = 0. Where is the center?

   (2, -3)
9. 6.

   Zee writes the edge of a pizza as x² + y² + 8x − 2y + 8 = 0. Where is the center?

   (-4, 1)
10. 7.

    Ari writes the edge of a pond as x² + y² − 10x − 4y + 20 = 0. Where is the center?

    (5, 2)
12. 8.

    Esme finishes completing the square: x² + 8x + 16. Which bracket squared is it?

    • (x + 16)²
    • (x + 4)²
    • (x + 8)²
    • (x − 4)²
13. 9.

    Jun finishes completing the square: x² − 12x + 36. Which bracket squared is it?

    Use the picture in question 8.

    • (x − 6)²
    • (x − 12)²
    • (x − 24)²
    • (x + 6)²
14. 10.

    Luz finishes completing the square: y² − 2y + 1. Which bracket squared is it?

    • (y + 1)²
    • (y − 4)²
    • (y − 2)²
    • (y − 1)²