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

Answer: x² + 6x + 9

Question 2: Factor the quadratic expression x² + 4x.

Answer: (x + 2)² - 4

Question 3: Expand the expression (x + 3)².

Answer: x² + 6x + 9

Question 4: Solve for x: x² + 4x + 1 = 0 using completing the square.

Answer: x = -2 ± √3

Question 5: Complete the square for the expression x² + 10x.

Answer: x² + 10x + 25

Question 6: Plot the graph of y = x² + 4x on the grid provided. (Draw the parabola on the grid.)

Answer: Parabola opening upwards, vertex at (-2, -4)

Question 7: Identify and correct the mistake: The expression x² + 8x was incorrectly expanded as (x + 4)².

Answer: Incorrect; (x + 4)² = x² + 8x + 16

Question 8: Express 3x² + 6x in the form a(x + b)² + c.

Answer: 3(x + 1)² - 3

Question 9: Solve the equation: x² + 2x - 8 = 0 by completing the square.

Answer: x = -1 ± √9, thus x = 2 or x = -4

Question 10: Find the value of x that satisfies (x + 5)² = 16.

Answer: x = -5 ± 4

Question 11: A ball is thrown upward such that its height after t seconds is given by h(t) = -t² + 4t + 2. Complete the square to find the maximum height and when it occurs.

Answer: Maximum height at t=2 seconds, height = 6