Question 1: Plot the graph of y = x² for x = -3, -2, -1, 0, 1, 2, 3. Record the points plotted.

Answer: (-3,9),(-2,4),(-1,1),(0,0),(1,1),(2,4),(3,9)

Question 2: Calculate the value of y when x = 4 and x = -4. Show your working.

Answer: 16

Question 3: Identify the mistake in the following student plot of y = x², where they plotted points for x = -2, -1, 0, 1, 2 but marked y-values as 4, 1, 0, 1, 4 incorrectly as y-values for x = -2 and 2.

Answer: They correctly plotted the points; no mistake. The y-values for x=-2 and 2 are 4, which is correct.

Question 4: Plot the parabola y = x² for x from -5 to 5. Identify the vertex and the axis of symmetry.

Answer: Vertex at (0,0), axis of symmetry x=0

Question 5: A student claims that the graph of y = x² is a straight line passing through (0,0). Explain why this is incorrect.

Answer: Because y = x² is a quadratic function, its graph is a parabola, not a straight line.

Question 6: Construct a table of values for y = x² for x = -2, -1, 0, 1, 2 and plot these points.

Answer: (-2,4),(-1,1),(0,0),(1,1),(2,4)

Question 7: Identify and correct the common mistake in plotting y = x², where students forget to square the x-values.

Answer: Students might plot y = x instead of y = x². Correct it by squaring the x-values.

Question 8: Given the points plotted: (-3,9), (-1,1), (0,0), (1,1), (3,9), find the missing point for x=2 assuming the shape is y = x².

Answer: 4

Question 9: A graph shows a parabola opening downwards. What mistake might the student have made if they were plotting y = x²? How can they fix it?

Answer: They plotted a negative y for some points. To fix it, they should ensure y = x² always produces positive y-values.

Question 10: Compare the graphs of y = x² and y = (x+2)². Describe the difference in their positions and how you can shift one to get the other.

Answer: The graph of y = (x+2)² is the graph of y = x² shifted 2 units to the left.

Question 11: Plot y = x² and y = 2x² on the same grid. Describe the difference in their shapes and how the coefficient affects the parabola.

Answer: y=2x² is narrower, the graph is stretched vertically by a factor of 2 compared to y=x².

Question 12: Identify a common misconception students have about the vertex of y = x² and explain how to correct it.

Answer: Many think the vertex is at the maximum point; it is actually at the minimum (0,0).