Question 1: Write the quadratic equation in standard form for a parabola with vertex at (2, -3) and passing through the point (4, 1).

Answer: y = a(x - 2)^2 - 3

Question 2: Calculate the value of y when x = 3 for the quadratic y = -2x^2 + 4x + 1. Show your working.

Answer: y = 3

Question 3: Plot the graph of y = 2(x - 1)^2 + 3 on the grid. (Describe key points and their coordinates.)

Answer: Vertex at (1, 3); points at (0, 5), (2, 5), (1, 2)

Question 4: Identify the axis of symmetry for the quadratic y = -x^2 + 6x - 5.

Answer: x = 3

Question 5: A ball is thrown upward so that its height after t seconds is modeled by y = -5t^2 + 10t + 2. How long does it take for the ball to reach its maximum height? Show your working.

Answer: t = 1

Question 6: Compare the graph of y = x^2 and y = -x^2. How do their shapes differ?

Answer: One opens upward, the other downward; same shape but inverted.

Question 7: If a quadratic passes through points (1, 2), (2, 3), and (3, 2), find the quadratic equation y = ax^2 + bx + c.

Answer: a = -1, b = 4, c = -1

Question 8: Identify and correct the mistake in the following graph: The parabola y = x^2 + 4x + 3 is graphed with vertex at (−2, 1).

Answer: Vertex at (−2, 1) is incorrect; vertex at (−4, 1)

Question 9: Challenge: Construct a quadratic on the grid with roots at x = -1 and x = 3, opening upward.

Answer: y = (x + 1)(x - 3) = x^2 - 2x - 3

Question 10: Explain how the value of 'a' affects the width and direction of the parabola in y = ax^2 + bx + c.

Answer: Positive 'a' opens upward, larger |a| makes it narrower; negative 'a' opens downward.