Question 1: Solve the inequality x² - 4x + 3 > 0 and draw the corresponding sign diagram.

Answer: x < 1 or x > 3

Question 2: Determine where the quadratic expression y = x² - 6x + 8 is negative. Sketch the sign diagram.

Answer: x between 2 and 4

Question 3: Construct the sign diagram for the inequality 2x² - 5x - 3 ≤ 0.

Answer: x between -0.5 and 3

Question 4: Given the quadratic y = -x² + 4x - 3, identify the intervals where y ≥ 0 and illustrate the sign diagram.

Answer: x between 1 and 3

Question 5: For the inequality x² + 2x - 8 < 0, determine the solution set and draw the sign diagram.

Answer: x between -4 and 2

Question 6: Plot the sign diagram for y = 3x² - 12x + 12 and state where y is positive.

Answer: x less than 2 or greater than 4

Question 7: Identify the interval where the quadratic x² - 5x + 6 is less than or equal to zero and illustrate the sign diagram.

Answer: x between 2 and 3

Question 8: Construct and interpret the sign diagram for the inequality -x² + 4x - 3 ≥ 0.

Answer: x between 1 and 3

Question 9: A quadratic function has roots at x = -1 and x = 4. Sketch the sign diagram for y = x² + 3x - 4 and state where y is positive.

Answer: x less than -1 or greater than 4

Question 10: Identify the common mistake when students interpret the sign diagram of y = x² - 9 and correct it.

Answer: Mistake: Confusing roots with solutions where quadratic is positive. Correction: Roots are points where quadratic equals zero; sign depends on intervals.

Question 11: Solve the inequality 4x² - 16 ≥ 0 and draw its sign diagram. Explain your steps.

Answer: x ≤ -2 or x ≥ 2