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

Answer: 9

Question 2: Plot the points corresponding to x = -2, 0, 2 on the grid for y = x².

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

Question 3: What is the value of y when x = -4?

Answer: 16

Question 4: Construct a parabola on the grid by plotting y = x² for x from -3 to 3.

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

Question 5: Calculate y when x = 5.

Answer: 25

Question 6: A student plots y = x² but marks the point (3, 6). Identify and correct the mistake.

Answer: The correct point should be (3, 9); mistake: y should be 9, not 6.

Question 7: Find the value of x when y = 25 in y = x².

Answer: x = ±5

Question 8: Plot the point where y = x² and y = 16. What are the x-values?

Answer: x = -4, 4

Question 9: A car accelerates so that its distance from a starting point follows y = x², where x is time in seconds. How far from the start is the car after 4 seconds?

Answer: 16 units

Question 10: Identify the common mistake: a student plots y = x² but draws a straight line passing through (0,0) and (2,4). Is this correct? Why or why not?

Answer: No, y = x² is a parabola, not a straight line. The line is only tangent at x=0, not the parabola.

Question 11: Challenge: If y = a(x - h)² + k, determine the vertex of the parabola y = (x + 2)² - 5.

Answer: Vertex at (-2, -5)

Question 12: Extend the understanding: Plot y = 3x² for x from -3 to 3. How does the parabola differ from y = x²?

Answer: It is wider and steeper; values are 3 times larger.