Question 1: Simplify the expression x² + 6x.

Answer: x² + 6x

Question 2: Complete the square for x² + 8x. Write it in the form (x + a)² + c.

Answer: (x + 4)² - 16

Question 3: Solve the equation x² + 10x + 25 = 0 by completing the square.

Answer: x = -5

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

Answer: See full answer key

Question 5: Factorise the quadratic expression x² + 7x + 12.

Answer: (x + 3)(x + 4)

Question 6: Given the quadratic x² + bx + c, if the roots are -2 and 4, find the values of b and c.

Answer: b = -2, c = -8

Question 7: Identify the mistake in the following solution: Completing the square for x² + 6x gives (x + 3)² + 0, which is incorrect.

Answer: Incorrect because completing the square for x² + 6x results in (x + 3)² - 9, not + 0.

Question 8: Express x² + 14x + 49 in completed square form.

Answer: (x + 7)²

Question 9: Solve for x: x² + 12x + 36 = 0 using completing the square.

Answer: x = -6

Question 10: Construct a quadratic in x² + bx form that has roots at x = -1 and x = 5. Write the quadratic in expanded form.

Answer: x² - 4x - 5

Question 11: Challenge: Derive the quadratic expression in x² + bx form that completes the square to (x - 3)² + 4.

Answer: x² - 6x + 13