Question 1: Find the critical values of the quadratic function y = x^2 - 4x + 3.

Answer: 1 and 3

Question 2: Determine where the quadratic y = 2x^2 - 8x + 6 is greater than zero.

Answer: x < 1 or x > 3

Question 3: Identify the critical points of y = -x^2 + 6x - 5 and state whether they are maxima or minima.

Answer: x=3; maximum

Question 4: Plot the graph of y = x^2 - 2x - 3. Mark the critical points.

Answer: x=1 and x=-1

Question 5: Solve the inequality x^2 - 5x + 6 ≤ 0 using critical values.

Answer: x=2 or x=3

Question 6: A ball is thrown such that its height in meters is given by h(t) = -4t^2 + 12t + 2. Find its critical points and interpret their meaning.

Answer: t=1.5; maximum height of 11 meters

Question 7: For the quadratic y = x^2 - 4x + c, find the value of c that makes the critical point a minimum at y = 0.

Answer: c=4

Question 8: Identify all the critical values of y = -3x^2 + 9x - 2 and determine the nature of the critical point.

Answer: x=1.5; maximum

Question 9: Construct a quadratic function with roots at x=2 and x=5 and find its critical point.

Answer: vertex at x=3.5

Question 10: A quadratic function is increasing on the interval [2, ∞). What can you conclude about its critical points?

Answer: critical point at x=2; minimum or maximum depending on the parabola's orientation

Question 11: Identify and correct the mistake: The critical points of y = x^2 + 4x + 5 are at x=-2.

Answer: Critical point at x=-2 is incorrect; it should be at x=-2.