Question 1: Simplify the expression: 3x² + 5x² - 2x².

Answer: 6x²

Question 2: If y = 4x² + 2, find the value of y when x = 3.

Answer: 38

Question 3: Rearrange the formula y = 2x² + 5 to solve for x².

Answer: x² = (y - 5)/2

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

Answer: Student plots on grid

Question 5: Construct a rectangle on the grid with length and width such that area = x² + 2x + 1.

Answer: Student constructs rectangle with sides x+1 and x+1

Question 6: Solve for x: 2x² = 50.

Answer: x = ±5√2

Question 7: A square garden has an area of 81m². Find the length of one side.

Answer: 9

Question 8: Explain why the expression x² + 6x + 9 can be written as (x + 3)².

Answer: Because x² + 6x + 9 is a perfect square trinomial, which factors as (x + 3)².

Question 9: A ball is thrown with height h = -4t² + 16t + 2, where t is time in seconds. Find the time when the ball reaches maximum height.

Answer: t = 2

Question 10: Identify the mistake in simplifying: 2x² + 3x² + x = 5x² + x.

Answer: Incorrect; the correct simplification is 5x² + x, so the mistake is in the initial expression.

Question 11: Challenge: If (x + 2)² = 25, find all possible values of x.

Answer: x = 3 or x = -7

Question 12: A rectangular park has an area of x² + 4x + 4 sq. meters. If the length is (x + 2) meters, find the width.

Answer: x + 2