Question 1: Simplify the expression: x² + 2x + 1.

Answer: (x + 1)²

Question 2: Rearrange the formula y = 3x² + 2 for x, expressing x in terms of y.

Answer: x = ±√( (y - 2) / 3 )

Question 3: Calculate the value of y when x = 4 in the formula y = x² + 4x + 3.

Answer: 35

Question 4: Factorize the quadratic expression: 4x² - 25.

Answer: (2x - 5)(2x + 5)

Question 5: Construct a quadratic equation with roots at x = 2 and x = -3, involving squared terms.

Answer: y = (x - 2)²(x + 3)² or expanded form

Question 6: Solve for x: 5x² = 45.

Answer: x = ±3

Question 7: Plot the graph of y = 2x² + 3 on the grid provided.

Answer: Student draws parabola opening upward, y-intercept at 3.

Question 8: Determine whether the point (2, 13) lies on the curve y = x² + 3x + 4.

Answer: Yes

Question 9: A rectangle has sides of length x and x + 2. If the area is x² + 4x + 4, find the dimensions of the rectangle.

Answer: Sides are x and x + 2, with area (x + 2)².

Question 10: Identify the common mistake in simplifying the expression x² + 2x + 1, and explain how to correct it.

Answer: Mistake: treating it as x² + 2x + 1 = (x + 1)² without factoring. Correction: Recognize it as a perfect square trinomial and factor as (x + 1)².

Question 11: Given the expression 9x² - 16, factor it completely.

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