THINKING/INQUIRY

(1). Determine the values of a and b in the relation y = ax² + bx + 7 if the vertex is located at (4, -5) (2 Marks)

(2). Determine the points of intersection of the line y = - 2x + 7 and the parabola of y = 2x² + 3x - 5. (2 Marks)

(3).Bob wants to cut a wire that is 60 cm long into two pieces. Then he wants to make each piece into a square. Determine how the wire should be cut so that the total area of the two squares is as small as possible. (2 Marks)

APPLICATION

(1). A baseball is hit from a height of 1 m. The height, h, of the ball in metres after t seconds can be modelled by h = -5t² + 9t + 1. Determine the maximum height reached by the ball. (3 Marks)

(2). While hiking along the top of a cliff, Harlan knocked a pebble over the edge. The height, h, in metres, of the pebble above the ground after t seconds is modelled by h = -5t² - 4t + 120.

a) How long will the pebble take to hit the ground? (2 Marks)

b) For how long is the height of the pebble greater than 95 m? (2 Marks)

(3). Joan kicked a soccer ball. The height of the ball, h, in metres, can be modelled by h = - 1.2x² + 6x, where x is the horizontal distance, in metres, from where she kicked the ball.

a) What was the initial height of the ball when she kicked it? How do you know? (3 Marks)

b) Complete the square to write the relation in vertex form. (2 Marks)

c) State the vertex of the relation. (2 Marks)

d) What does each coordinate of the vertex represent in this situation? (2 Marks)

e) How far did Joan kick the ball? (2 Marks)

(4).A trained stunt diver is diving off a platform that is 15 m high into a pool of water that is 45 cm deep. The height, h, in metres, of the stunt diver above the water is modelled by h = - 4.9t² + 1.2t + 15 , where t is the time in seconds after starting the dive.

a) How long is the stunt diver above 15 m? (2 Marks)

b) How long is the stunt diver in the air? (2 Marks)