🧠 Quiz: Completing the Square

🧠 Quiz: Completing the Square

1. Rewrite \(x^2 + 6x + 5\) by completing the square.

\((x+3)^2 - 4\) \((x+2)^2 - 1\) \((x+3)^2 + 4\) \((x+2)^2 + 1\)

2. Solve \(x^2 + 4x = 5\) by completing the square.

\(x = -2 \pm \sqrt{9}\) \(x = -2 \pm \sqrt{5}\) \(x = 2 \pm \sqrt{5}\) \(x = -2 \pm \sqrt{1}\)

3. Which constant must be added to \(x^2 + 8x\) to complete the square?

16 8 4 32

4. Rewrite \(x^2 - 10x + 21\) by completing the square.

\((x-5)^2 - 4\) \((x-5)^2 + 4\) \((x-10)^2 - 79\) \((x-5)^2 - 21\)

5. Solve \(x^2 + 2x - 3 = 0\) using completing the square.

\(x = -1 \pm 2\) \(x = 1 \pm \sqrt{2}\) \(x = -1 \pm \sqrt{4}\) \(x = 3 \pm \sqrt{2}\)

6. Which quadratic is a perfect square trinomial?

\(x^2 + 6x + 9\) \(x^2 + 5x + 6\) \(x^2 + 4x + 8\) \(x^2 + 2x + 5\)

7. Solve \(x^2 - 6x + 5 = 0\) by completing the square.

\(x = 3 \pm \sqrt{4}\) \(x = 2 \pm \sqrt{5}\) \(x = 3 \pm \sqrt{9}\) \(x = -3 \pm \sqrt{5}\)

8. Which constant completes the square for \(x^2 - 12x\)?

36 12 24 6

9. Rewrite \(x^2 + 10x + 21\) by completing the square.

\((x+5)^2 - 4\) \((x+5)^2 + 4\) \((x+10)^2 - 79\) \((x+5)^2 - 21\)

10. Which constant completes the square for \(x^2 + 14x\)?

49 14 7 28