Question 1: Simplify the expression by completing the square: x² + 6x.

Answer: (x+3)^2 - 9

Question 2: Rewrite the quadratic expression x² + 10x + 21 in completed square form.

Answer: (x+5)^2 - 4

Question 3: Plot the graph of y = x² + 4x + 1 on the grid.

Answer: Students plot on grid

Question 4: A ball is thrown upwards such that its height h(t) (in meters) is given by h(t) = -4t² + 8t + 2. Rewrite h(t) in completed square form to find its maximum height.

Answer: h(t) = -4(t - 1)^2 + 6

Question 5: Identify the mistake: Student claims that x² + 8x simplifies to (x + 4)^2. Correct the mistake.

Answer: x² + 8x = (x + 4)^2 - 16

Question 6: Solve for x: x² + 6x = 0. Use completing the square.

Answer: x=0 or x=-6

Question 7: A rectangular garden has a length that is 4 meters longer than its width. The area is given by A = x² + 4x. Write an expression for the length in terms of x and find the maximum possible area.

Answer: Length = x + 4; Maximum area when x = -2, Area = 4

Question 8: Factorize the quadratic: x² + 12x + 36.

Answer: (x + 6)^2

Question 9: Construct a quadratic expression in x² + bx form that has roots at x = -2 and x = 3. Write the expanded form.

Answer: x² - x - 6

Question 10: Identify and correct the error: Student rewrites x² + 14x as (x + 7)^2 without subtracting 49.

Answer: Correct form: (x + 7)^2 - 49

Question 11: A projectile's height after t seconds is modeled by h(t) = -t² + 6t + 2. Rewrite in completed square form and determine the time at which maximum height occurs.

Answer: h(t) = -(t - 3)^2 + 11; maximum at t=3 seconds