Question 1: Plot the graph of y = 2x + 1 and y = x^2 - 4. Determine the coordinates of their intersection points.

Answer: [intersect points coordinates]

Question 2: Using the graph from Question 1, estimate the x-values where the curves intersect.

Answer: Approximately x = -1.5 and x = 2

Question 3: Construct a graph showing y = -x^2 + 3x and y = 4x - 1. Find the intersection points.

Answer: [coordinates of intersection]

Question 4: Plot the graph of y = x^2 and y = 2x + 3. Use the graph to find approximate solutions to the simultaneous equations.

Answer: [approximate intersection points]

Question 5: A car's path is modeled by y = -x^2 + 4x, and its route is also described by y = 2x + 1. Sketch both graphs and find where the paths intersect.

Answer: [coordinates of intersection]

Question 6: Plot y = x^2 - 2x and y = -x + 3. Identify the approximate intersection points and verify algebraically.

Answer: [coordinates]

Question 7: Plot y = 3x^2 - x and y = 2x + 5. How many solutions do the graphs have? Estimate their x-values.

Answer: Two solutions, approximately x ≈ -1 and x ≈ 2.5

Question 8: Construct the graphs of y = x^2 + 4x + 3 and y = -x^2 + 2x + 1. Find their intersection points.

Answer: [coordinates]

Question 9: On the grid, plot y = x^2 and y = 4x - 3. Use the graph to estimate the solutions to the simultaneous equations.

Answer: [approximate solutions]

Question 10: Error Analysis: Common mistake is to incorrectly identify intersection points or to misplot the graphs. Look at the graph of y = x^2 + 2x and y = 3x + 4. What is a common mistake students might make, and how can it be corrected?

Answer: Common mistake: Misreading the intersection points or plotting points inaccurately. Correction: Double-check the plotted points and verify algebraically.