The graph below shows a company’s profit f(x), in dollars, depending

| August 30, 2017

Question 1 (Essay Worth 10 points)


The graph below shows a company’s profit f(x), in dollars, depending on the price of pencils x, in dollars, being sold by the company.

graph of quadratic function f of x having x intercepts at ordered pairs negative 0, 0 and 10, 0. The vertex is at 5, 160

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing and what do they represent about the sale and profit? (5 points)

Part B: If at one time the profit of the company was at least one hundred dollars, what domain could possibly produce this profit? (2 points)

Part C: What is an approximate average rate of change of the graph from x = 2 to x = 5 and what does this rate represent? (3 points)

Question 2 (Essay Worth 10 points)


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:

Time (t) g(t)
0 0
0.4 7.04
0.6 8.64
0.75 9
1.0 8
1.5 0

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)

Question 3 (Essay Worth 10 points)


A sandbag was thrown downward from a building. The function f(t) = -16t2 – 32t + 384 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)

Question 4 (Essay Worth 10 points)


A quadratic equation is shown below:

9×2 – 36x + 36 = 0

Part A: Describe the solution(s) to the equation by just determining the discriminant. Show your work. (3 points)

Part B: Solve 2×2 – 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used.(4 points)

Part C: Solve 3×2 – 12x + 2 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)

Question 5 (Essay Worth 10 points)

[09.05, 09.06]

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 90 feet with an initial velocity of 50 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) = 28 + 48.8t 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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