Expanded Equation Quiz (5 Questions)

1. Expand the standard equation (x−1)² + (y+2)² = 9

2. True or False: Expanded form always contains x² and y² terms.

3. Identify center and radius from expanded form x² + y² − 6x + 8y − 11 = 0

4. Convert x² + y² + 4x − 6y + 9 = 0 to standard form.

5. Give a real-world example where knowing expanded form is useful.

Answer Key

1. x² − 2x + 1 + y² + 4y + 4 = 9 → x² + y² − 2x + 4y − 4 = 0

2. True

3. Complete the square: (x−3)² − 9 + (y+−4?)² − ? → center = (3,−4), radius = √? (step-by-step to solve in full)

4. Complete square: (x+2)² − 4 + (y−3)² − 9 + 9 = 0 → (x+2)² + (y−3)² = 4

5. Physics problems, radar range, engineering designs, circular tracks, satellite coverage