APPLICATION

(1). A video tracking device recorded the height, h, in metres, of a baseball after it was hit. The data collected can be modelled by the relation h = - 5 (t - 2) ²+ 21 , where t is the time in seconds after the ball was hit.

a) Sketch a graph that represents the height of the baseball. (2 Marks)

b) What was the maximum height reached by the baseball? (2 Marks)

c) When did the baseball reach its maximum height? (2 Marks)

d) At what time(s) was the baseball at a height of 10 m? (2 Marks)

e) Approximately when did the baseball hit the ground? (2 Marks)

KNOWLEDGE AND UNDERSTANDING

(1). Sketch the graph of each equation by applying a transformation to the graph of y = x². Use a separate grid for each equation, and start by sketching the graph of y = x². (2 Marks each)

a) y = 3x²

b) y = - 0.5x²

c) y = -2x²

d) y = x²

(e) y = -3/2 x²

(f) y = 5x²

(2).The following transformations are applied to a parabola with the equation. Determine the values of h and k, and write the equation in the form y = (x - h)² + k. (2 Marks each)

a) The parabola moves 3 units right.

b) The parabola moves 4 units down.

c) The parabola moves 2 units left.

d) The parabola moves 5 units up.

e) The parabola moves 7 units down and 6 units left.

f) The parabola moves 2 units right and 5 units up.

(3). Describe the transformations that are applied to the graph of to obtain the graph y = x² of each quadratic relation. (2 Marks each)

(a). y = x² + 5

(b). y = (x - 3)²

(c) y = - 3x²

(d) y = (x + 7)²

(e). y = x²

(f). y = (x + 6)² + 12