Question 1: Solve for x: x^2 + 6x + 5 = 0 using completing the square.

Answer: x = -1 ext{ or } x = -5

Question 2: Complete the square for the quadratic expression: x^2 + 4x + 1.

Answer: (x + 2)^2 - 3

Question 3: Find the roots of 2x^2 - 8x + 6 = 0 by completing the square.

Answer: x = 1 ext{ or } x = 3

Question 4: Plot the graph of y = (x + 3)^2 - 4. Use the grid to sketch the parabola.

Answer: See full answer key

Question 5: Construct a triangle with sides fitting the equation (x - 2)^2 + (y + 1)^2 = 25 on the grid. Explain how the completed square form relates to this circle's radius.

Answer: See full answer key

Question 6: Solve x^2 - 4x - 5 = 0 by completing the square and check your solutions.

Answer: x = 5 ext{ or } x = -1

Question 7: A quadratic expression is written as x^2 + 10x + 16. Complete the square and write it in vertex form.

Answer: (x + 5)^2 - 9

Question 8: A ball is thrown and its height in meters after t seconds is modeled by h(t) = -t^2 + 4t + 1. Use completing the square to find the time when the ball reaches its maximum height.

Answer: t = 2

Question 9: Solve 3x^2 + 12x + 7 = 0 by completing the square, and interpret the solutions.

Answer: x = -2 + rac{ ext{i} oot{3}}{3} ext{ or } x = -2 - rac{ ext{i} oot{3}}{3}

Question 10: Identify and correct the mistake in completing the square for x^2 + 2x = 8.

Answer: See full answer key

Question 11: Extend: Given the equation x^2 + 8x + 12 = 0, complete the square and determine the solutions.

Answer: x = -4 ext{ or } x = -3