Question 1: Solve for x: 2x² + 3x - 2 = 0 using the quadratic formula.

Answer: x = 0.5 or x = -2

Question 2: Calculate the solutions of 4x² - 4x = 0.

Answer: x = 0 or x = 1

Question 3: Construct a quadratic graph for x² - 4x + 3 = 0 on the grid.

Answer: parabola crossing x-axis at x=1 and x=3

Question 4: Find the roots of 3x² + 2x - 1 = 0.

Answer: x = 0.25 or x = -/3

Question 5: Explain why the quadratic formula can find solutions even when the quadratic does not factor easily.

Answer: Because it is derived from completing the square, which always works for any quadratic.

Question 6: Solve for x: x² - 6x + 9 = 0.

Answer: x = 3 (double root)

Question 7: Find the solutions to 5x² + 0x - 20 = 0.

Answer: x = 2 or x = -2

Question 8: A ball is thrown upwards following the path y = -2x² + 4x + 1. When does it hit the ground (y=0)?

Answer: x = -0.25 or x = 1.25

Question 9: Determine if the quadratic 6x² + 2x + 5 = 0 has real solutions and explain.

Answer: Discriminant is negative, so no real solutions.

Question 10: Solve 7x² - 14x + 7 = 0 by the quadratic formula.

Answer: x = 1 (double root)

Question 11: Identify the mistake in solving x² + 4x + 4 = 0 by factoring, and correct it.

Answer: Mistake: Assuming it factors as (x+2)(x+2), which is correct, but missing the fact it is a perfect square, so root is x=-2.

Question 12: Plot the graph of y = x² - 2x - 3 on the grid and identify the roots.

Answer: Roots at x = -1 and x = 3