Question 1: Given the quadratic function y = x^2 - 4x + 3, find its critical values.

Answer: 1 and 3

Question 2: Determine the critical values of the quadratic expression x^2 + 6x + 8.

Answer: -3 and -1

Question 3: Calculate the critical points where the quadratic y = 2x^2 - 8x + 6 intersects its vertex.

Answer: x=2

Question 4: Plot the graph of y = x^2 - 4x + 3. Mark the critical values on the x-axis.

Answer: x=1 and x=3

Question 5: Construct a quadratic graph with critical values at x = -2 and x = 4. Write the quadratic function equation.

Answer: y = a(x + 2)(x - 4) with a chosen, e.g., 1

Question 6: Solve the inequality y > 0 for y = x^2 - 5x + 6, based on its critical values.

Answer: x < 2 or x > 3

Question 7: A ball is thrown such that its height h(t) = -t^2 + 4t + 2, where t is time. Find the critical times when the height reaches its maximum.

Answer: t=2

Question 8: Determine whether the quadratic y = 3x^2 - 12x + 5 is positive or negative between its critical values.

Answer: Positive between the critical values

Question 9: Find the critical values of y = x^2 - 2x - 8 and determine the intervals where y is less than zero.

Answer: x=-2 and x=4; y<0 between x=-2 and x=4

Question 10: An object’s height over time is modeled by h(t) = -2t^2 + 8t + 5. Find the critical times for maximum height, and state the maximum height.

Answer: t=2; maximum height h=13

Question 11: Identify and correct the mistake in this statement: 'Critical values are always the roots of the quadratic and the maximum or minimum points of the parabola.'

Answer: Critical values are not always roots; they are points where the quadratic changes concavity (vertex or turning points).

Question 12: Challenge: Given y = 2x^2 - 4x + 1, find the critical values and determine the nature (max/min) of the vertex.

Answer: x=1; minimum