Question 1: Plot the graph of y = 2x² - 4x + 1 on the grid. Identify the vertex coordinates.

Answer: Vertex at (1, -1)

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

Answer: 6

Question 3: Determine the axis of symmetry for y = 3x² - 6x + 5.

Answer: x=1

Question 4: Identify whether the parabola y = -x² + 4x - 3 opens upwards or downwards.

Answer: downwards

Question 1: A ball is thrown such that its height in meters after t seconds is modeled by y = -5t² + 20t + 2. Find the maximum height and the time it occurs.

Answer: Maximum height: 12 meters at t=2 seconds

Question 2: Given y = x² - 6x + 10, find the coordinates of the vertex and describe the parabola's shape.

Answer: Vertex at (3, 1), opens upwards

Question 3: Explain how changing the value of 'a' in y = ax² + bx + c affects the width and direction of the parabola.

Answer: Increasing |a| makes the parabola narrower; negative a opens downward, positive upward.

Question 4: Determine the roots of y = 2x² - 8x + 6 using the quadratic formula.

Answer: x=1 and x=3

Question 1: A manufacturer finds that the profit P (in thousands of dollars) from selling x units of a product is modeled by P = -0.5x² + 4x - 10. Find the number of units to maximize profit and the maximum profit.

Answer: Max profit at 4 units; profit = 2 thousand dollars

Question 2: A satellite is launched from the ground, reaching a height modeled by y = -4t² + 16t, where t is time in seconds. When does the satellite reach its maximum height and what is it?

Answer: Maximum height at t=2 seconds, height=16 meters

Question 1: Given y = -2x² + 8x + 5, find the x-coordinate of the point where the parabola intersects the x-axis, if real solutions exist.

Answer: x= -0.38 or x=4.38 (approximate)

Question 2: Construct the graph of y = 0.5x² - 3x + 4. Determine the vertex, axis of symmetry, and intercepts. Describe how these features relate to the graph's shape.

Answer: Vertex at (3, -1.5), axis x=3, y-intercept at (0,4), x-intercepts at approximately 0.94 and 5.06; parabola opens upwards, narrower than y= x²

Question 1: A student claims that y = 3x² + 6x + 2 has its vertex at (-1, 5). Identify and correct the mistake.

Answer: Vertex at (-1, -1), not ( -1, 5)

Question 2: A graph shows a parabola opening downwards with vertex at (2, 3). The student wrote the equation as y = x² + 4x + 5. Identify the mistake and provide the correct quadratic equation.

Answer: Incorrect vertex; correct equation y = -x² + 4x + 3