Question 1

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?

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

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?

Question 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:

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)?

Part B: Which function has a greater x-intercept? What do the x-intercepts of the graphs of f(t) and g(t) represent?

Part C: Determine the y-intercepts of both functions and explain what this means in the context of the problem.

Question 3

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.

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?

Part C: Use your answer in part B to determine the axis of symmetry for f(x)?

Question 4

A quadratic equation is shown below:

9x2 - 36x + 36 = 0

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

Part B: Solve 2x2 - 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used.

Part C: Solve 3x2 - 12x + 2 = 0 by using a method different from the one you used in Part B. Show the steps of your work.

Question 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 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.

Part B: What is the maximum height that the projectile will reach? Show your work.

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?

Part D: Do H(t) and g(t) intersect when the projectile is going up or down and how do you know