labrador-leaps-over-a-hurdle-The-function-f-t-represents-the-height-of-the-Labrador-above-the-ground-in-inches-at-t-seconds-
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| 2. A Labrador leaps over a hurdle. The function f(t) represents the height of the Labrador above the ground, in inches, at t seconds:
f(t) = -16t2 + 20t A foxhound jumps over the same hurdle. The table shows the height of the foxhound above the ground g(t), in inches, at t seconds:
Part A: Compare and interpret the maximum of f(t) and g(t)? (4 points) Part B: Which function has a greater x-intercept? What do the x-intercepts of the graphs of f(t) and g(t) represent? (4 points) Part C: Determine the y-intercepts of both functions, and explain what this means in the context of the problem. (2 points) |
| 3. A sandbag was thrown downward from a building. The function f(t) = -16t2 – 64t + 80 shows the height f(t), in feet, of the sandbag after t seconds:
Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function. (4 points) Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph? (4 points) Part C: Use your answer in part B to determine the axis of symmetry for f(x)? (2 points) |
| 4. A quadratic equation is shown below:
x2 + 5x + 4 = 0 Part A: Describe the solution(s) to the equation by just determining radicand. Show your work. (3 points) Part B: Solve 4x2 -12x + 5 = 0 using an appropriate method. Show the steps of your work, and explain why you chose the method used. (4 points) Part C: Solve 2x2 -10x + 3 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points) |
| 5. The function H(t) = -16t2 + vt + s shows the height H(t), in feet, of a projectile launched vertically from s feet above the ground after t seconds. The initial speed of the projectile is v feet per second.
Part A: The projectile was launched from a height of 96 feet with an initial velocity of 80 feet per second. Create an equation to find the time taken by the projectile to fall on the ground. (2 points) Part B: What is the maximum height that the projectile will reach? Show your work. (2 points) Part C: Another object moves in the air along the path of g(t) = 31 + 32.2t where g(t) is the height, in feet, of the object from the ground at time t seconds. Use a table to find the approximate solution to the equation H(t) = g(t), and explain what the solution represents in the context of the problem? [Use the function H(t) obtained in Part A, and estimate using integer values] (4 points) Part D: Do H(t) and g(t) intersect when the projectile is going up or down, and how do you know? (2 points) |
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