1. www.thevisualclassroom.com A picture frame measures 8 cm by 12 cm. We wish to add a border of equal width around the frame. The area of the border must equal to the area of the frame. Determine the width of the border correct to one decimal place. 8 cm 12 cm x x x x Let x = width of the picture frame. Area of picture: 8 cm × 12 cm = 96 cm 2 Area of picture and frame: 192 cm 2 Equation: (2x + 8)(2x + 12) = 192 cm 2 2x + 8 2x + 12 4x 2 + 24x + 16x + 96 = 192 4x 2 + 40x + 96 – 192 = 0 4x 2 + 40x – 96 = 0

2. www.thevisualclassroom.com 4x 2 + 40x – 96 = 0 4(x 2 + 10x – 24) = 0 a = 1, b = 10 and c = – 24 x 1 = 2 x 2 = – 12 The width of the frame is 2cm.

3. www.thevisualclassroom.com A bullet is fired vertically into the air at an initial velocity of 80 m/s. The height in metres is given by the h = 80t – 5t 2. (t = sec.) Find the time it takes the bullet to reach 100 m. h = –5t 2 + 80t 100 = –5t 2 + 80t 5t 2 – 80t + 100 = 0 5(t 2 – 16t + 20) = 0 a = 1, b = – 16 and c = 20 t = 1.2 sec or 14.8 sec

4. www.thevisualclassroom.com A picture frame measures 15 cm by 25 cm. We wish to add a border of equal width around the frame. The area of the border must equal to the area of the frame. Determine the width of the border correct to one decimal place. 15 cm 25 cm x x x x Let x = width of the picture frame. Area of picture: 15 cm × 25 cm = 375 cm 2 Area of picture and frame: 750 cm 2 Equation: (2x + 15)(2x + 25) = 750 cm 2 2x + 15 2x + 25 4x 2 + 50x + 30x + 375 = 750 4x 2 + 80x + 375 – 750 = 0 4x 2 + 80x – 375 = 0

5. www.thevisualclassroom.com 4x 2 + 80x – 375 = 0 a = 4, b = 80 and c = – 375 x 1 = 3.9 x 2 = – 23.92 The width of the frame is 3.9 cm.