Question 1: Plot the graph of y = x² when x ranges from -3 to 3.

Answer: Correct parabola shape passing through (-3,9), (0,0), (3,9)

Question 2: Calculate y when x=2 for the quadratic y = 3x² - 4x + 1.

Answer: 3(2)^2 - 4(2) + 1 = 12 - 8 + 1 = 5

Question 3: Identify the coefficients a, b, c in the quadratic y=2x² + 4x - 6.

Answer: a=2, b=4, c=-6

Question 4: Construct the parabola of y = -x² + 2x + 3 on the grid. Mark the vertex and intercepts.

Answer: Vertex at (1,4); y-intercept at (0,3); x-intercepts at approximately (-0.56,0) and (2.56,0)

Question 5: If the quadratic y = 4x² + 2x + 1 is graphed, what is the minimum value of y?

Answer: Minimum at vertex x = -b/2a = -2/8 = -0.25; y = 4(-0.25)^2 + 2(-0.25) + 1 = 4(0.0625) - 0.5 + 1 = 0.25 - 0.5 + 1 = 0.75

Question 6: Plot the quadratic y = -2x² + 4x - 1 and identify its axis of symmetry.

Answer: Axis of symmetry at x = -b/2a = -4/(-4) = 1

Question 7: A parabola opens downward with vertex at (2, 5). Write its general quadratic form assuming the vertex form is y = a(x - 2)² + 5.

Answer: y = a(x - 2)² + 5; for example, with a = -1, y = -(x - 2)² + 5

Question 8: Determine whether the quadratic y = 3x² + 6x + 2 has a maximum or minimum point, and find its coordinates.

Answer: Minimum point at x = -b/2a = -6/6 = -1; y = 3(-1)^2 + 6(-1) + 2 = 3 - 6 + 2 = -1

Question 9: A quadratic function models the height of a ball: y = -5x² + 10x + 2. Find the maximum height and when it occurs.

Answer: Maximum at x = -b/2a = -10/(-10) = 1; y = -5(1)^2 + 10(1) + 2 = -5 + 10 + 2 = 7

Question 10: Identify and correct the mistake: The quadratic y = x² - 4x + 3 has its vertex at (2, -1).

Answer: Correct. Vertex at x = 2, y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1