Revenue Models and Projectile Motion

Professor Shannon Gracie covers Section 3.4 from 'Pre-calculus Enhanced with Graphing Utilities' by Sullivan and Sullivan. The video includes examples of building quadratic models from descriptions, calculating the vertex of quadratic functions, modeling revenue as a function of quantity, maximizing area with fencing constraints, solving a parabolic arch problem, and analyzing projectile motion to find maximum height and distance.

What is the first step in finding the vertex of a quadratic function?

• Find the y-intercept.

• Evaluate the function at zero.

• Use the formula -b/2a.

• Set the function equal to zero.

In the context of revenue models, what does the variable 'R' typically represent?

• Revenue

• Resistance

• Radius

• Rate

How do you determine the domain of a revenue function?

• By ensuring the number of units and price are non-negative.

• By finding the range of prices.

• By calculating the maximum revenue.

• By setting the function equal to zero.

What is the revenue if 100 units are sold, given the revenue function R(x) = -13x + 100x?

• $8,000.00

• $5,000.00

• $7,000.00

• $6,666.67

What quantity of items sold will maximize the revenue?

• 100 items

• 150 items

• 200 items

• 250 items

What price should be charged to maximize revenue?

• $70

• $60

• $50

• $40

In a fencing problem, if a farmer has 2000 meters of fencing, what is the maximum area that can be enclosed?

• 400,000 square meters

• 500,000 square meters

• 600,000 square meters

• 700,000 square meters

What is the equation of a parabola with a vertex at (0, 25) and a span of 120 ft?

• f(x) = 1/100 x^2 + 25

• f(x) = -1/144 x^2 + 25

• f(x) = 1/144 x^2 + 25

• f(x) = -1/100 x^2 + 25

What is the height of the parabolic arch at x = 10 ft?

• 22.2 ft

• 18.5 ft

• 24.3 ft

• 20.0 ft

At what horizontal distance is the height of a projectile maximum if fired at 45° with 100 ft/s?

• 156.25 ft

• 200.00 ft

• 250.00 ft

• 300.00 ft