Quadratic equation
1. Use the completing the square method to express the following equations in vertex form. State the vertex and whether the parabola has a maximum or minimum value. (4 marks each) a. = x2 - 10x + 3 b. y = - 2 2 + 12x + 2 y = 4m2 + 32m + 33 2. The height, h metres, of a flare as a function of time, t seconds, because the flare was fired from a boat, can be modeled by the function: (6 marks) h = -5.25 (t t - 4)2 + 86 a. What was its height when it was fired? b. What was the maximum height of the flare? c. What was the time when the flare reached its maximum height? d. How many seconds after it was fired did the flare hit the water? . The path of a soccer ball can be given by the quadratic function: h - 29.4t - 4.912, where t is the time in seconds and h is the height in metres. (5 marks) a. Put the function in vertex form, and state the maximum height reached by the ball. b. How many seconds did it take to reach this height? - A police officer is investigating a crime which occurred in a rectangular field next to a building He wants to seal the three sides of the area around the scene with 300 m of yellow police tape What is the maximum area that he can enclose, and what are the dimensions of this area? Hint (6 marks) 5. A parabola passes through the point (3, 5) on its way to the vertex at (7, 11). Determine the equation in vertex form that represents this parabola. (3 marks) Solve for a in the following quadratic equations by factoring. a. x2 8x + 16 = 0 (3 marks) b. x2 + 14x = 0 (4 marks) C. 6x2 - 7x 3 = 0 (4 marks) d. x2 (2)x + 3 =0 (4 marks) 2. Solve for a in the following quadratic equations using the formula. State your answers in fraction or whole number form, or round decimals to the nearest tenth. (3 marks each) a. 5x2 8x 4 = 0 b. 3x2 + 2 - 4x c. 9x 2 + 12x + 4 = 0 Remember to include a LET statement to define your variable and concluding statement. 1. The sum offan integer and five times its square is 174. Find the integer. (5 marks) 2. A right triangle has a height 8 cm more than twice the length of the base. If the area of the triangle is 96 cm2, what are the dimensions of the triangle. (6 marks) 3. A baseball is hit from a height of 0.8 m. After t seconds, its height, h metres, is given by the equation h -5t2 + 20t + 0.8. How long does the ball stay at least 15 m above the ground? (5 markel 4. An art dealer advises that, for the best display of a painting, the area of the frame should be ( ) the area of the painting. Determine the best width of the frame for a painting 20 cm by 20 cm, if the width is to be the same on all sides. Round your answer to the nearest tenth. (6 marks) . A rectangular flower bed is to be created so that the length is 3 m more than the width. If the length of the diagonal of the flower bed is 15 m, determine the length and the width
