Question 1: Calculate the value of y when x = 3 in the equation y = x².

Answer: 9

Question 2: Find the value of x when y = 16 in the equation y = x².

Answer: 4

Question 3: Plot the points corresponding to x = -2, 0, and 3 on the grid. Then sketch the parabola y = x².

Answer: Points (-2, 4), (0, 0), (3, 9) plotted; parabola sketched through these points.

Question 4: Construct a parabola on the grid that passes through the points (1,1), (2,4), and (3,9).

Answer: Parabola y = x² passing through these points.

Question 5: If x = -1.5, what is the value of y in y = x²?

Answer: 2.25

Question 6: Explain why the graph of y = x² is symmetric about the y-axis.

Answer: Because for every x, y = x² is the same as for -x, making the parabola mirror itself across the y-axis.

Question 7: A ball is thrown upward such that its height in meters after t seconds is given by y = t². Plot the points for t = 0, 1, 2 on the grid and describe the shape.

Answer: Points (0,0), (1,1), (2,4); the graph is a parabola opening upwards.

Question 8: Calculate the x-values where y = 25 in y = x².

Answer: ±5

Question 9: Identify and correct the mistake: The graph of y = x² passes through (2,4) and (-2,4), so it is a straight line.

Answer: The mistake is assuming y = x² is a straight line; it is a parabola, not a line.

Question 10: Challenge: Find the equation of the parabola passing through points (1,1), (2,4), and (4,16).

Answer: y = x²