Question 1: Plot the graph of y = 2x + 1. Label the line.

Answer: Students plot the line y=2x+1 on the grid.

Question 2: Plot the graph of y = x² - 3. Label the parabola.

Answer: Students plot y=x²-3 on the grid.

Question 3: Using the grid, find the point where y=2x+1 and y=x² - 3 intersect.

Answer: x ≈ 2, y ≈ 5 (approximate intersection point)

Question 4: Construct the graphs of y = -x + 4 and y = (x-2)² - 1 on the same grid. Find their point(s) of intersection.

Answer: Intersection at approximately (1, 3)

Question 5: Plot y = x² + 2x. Draw the curve clearly.

Answer: Students plot y=x²+2x.

Question 1: The line y = -x + 5 intersects with the parabola y = x² - 1. Find the approximate coordinates of the intersection point(s). Explain how you found it using the graph.

Answer: Approximate intersection at (2, 3). Explanation: By plotting both, the intersection occurs near x=2, y=3.

Question 2: A roller coaster track follows y = x² - 4x + 3. The height y in meters. Construct the graph for x from 0 to 4, then determine where the height is 0.5 meters.

Answer: Approximate x ≈ 0.5 and x ≈ 3.5 where y=0.5

Question 3: Explain how the shape of the quadratic affects the number of solutions when intersected with a line.

Answer: If the parabola opens upward, there can be zero, one, or two solutions depending on the line's position.

Question 1: A car's speed increases following y = x²/4 + 10, where y is speed in km/h and x is time in seconds. A linear line y = 2x + 10 represents a different speed pattern. Graph both from x=0 to 10 seconds. When do the speeds match?

Answer: Approximately at x ≈ 4 seconds.

Question 1: Construct the graphs of y = x² - 2x - 3 and y = 3x - 4. Using the graph, estimate the solutions to the equations. Then, explain how the quadratic's vertex influences the number of solutions.

Answer: Solutions approximately at x ≈ -1, 3. The vertex x ≈ 1, y = -4 influences the intersection points.

Question 2: Design a quadratic function y = ax² + bx + c that intersects the line y = x + 2 at exactly two points, one point, and no points. Sketch the graphs on the grid.

Answer: Various coefficients create different intersections; sketches should show these scenarios.

Question 1: A student plots y=2x+1 and y=(x-1)²+3 but mistakenly labels the parabola as y=x²+3. Identify the error and explain how it affects finding the intersection points.

Answer: The actual parabola is shifted right by 1, up by 3; labeling it incorrectly leads to wrong intersection points.

Question 2: A graph shows a line y=3x+2 and a parabola y= x² - 4x + 1. The student claims they intersect at (2, 8). Check this claim and correct if necessary.

Answer: At x=2, y=3(2)+2=8; parabola at x=2: y=4-8+1=-3. No, they do not intersect at (2,8).