Chapter 3 Review Sheet

Chapter 3 – Review Sheet

3.1 Linear Functions, Their Properties, and Linear Models

Examples

1. Use the data table to a) find the average rate of change, b) say whether it is increasing, decreasing or constant and c) then build the model. What is Break Even point mean?

2. LeBron wants to start a new basketball shoe company. He expects the yearly fixed costs to be $375,000 and the cost per pair of sneakers to be $54. Write a model to describe total costs as a function of number of sneakers made.

3.2 Building Linear Models from Data

Examples

3. LeBron wants to show that his shoes make you jump higher. He runs an experimental study and wants to make a model of height with his shoes, L, and height without his shoes, W. a)Graph the line on a scatterplot and b) express the relationship with functional notation. c) How high would you expect with LeBron’s shoes if you currently jump 5.5 feet?

3.3 Quadratic Functions and Their Properties

Examples

4. Dustin wants to figure out the angle of the hit to maximize the distance that the ball goes. Use the table to a) graph the line on a scatterplot and b) express the relationship with functional notation. Finally, c) find the distance that you would expect if you hit the ball at a 63 angle. (The model uses a constant bat velocity of 90mph)

3.4 Building Quadratic Models from Verbal Descriptions and from Data

Examples

(inaddition to the worksheet)

5. LeBron expects his shoes to sell according to the linear model of x = 20,000 – 74p, where x is the number of shoes sold and p is the price. a) Find the maximum revenue that you could achieve and b) the ideal price to set the shoe.

6. A contractor is to build a warehouse whose rectangular floor will have an area of 400 square feet. The warehouse will be separated into two rectangular rooms by an interior wall. The cost of the exterior walls is $175 per linear foot and the cost of the interior wall is $125 per linear foot. Express the contractor’s cost for building walls, C, as a function of the dimensions of the warehouses’ rectangular floor, x. (Hint: let x be the interior of the wall).

6B. The following data represent the percentage of the population in a certain country

aged 40 or older whose age is x who do not have a college degree of some type.

Find a quadratic model that describes the relationship between age and percentage of

the population that do not have a college degree. Use the model to predict the

percentage of 53-year-olds that do not have a college degree

3.5 Inequalities Involving Quadratic Functions

Examples

Solve each inequality.

7. x2 – 3x – 10 ≤ 08. x(x + 1) > 209. 25x2 + 16 < 40x

Be able to do this by hand:

10. Graph the equation: y = -x/3 + 2. (find the intercept and move along the slope)

11. Graph the equation: y = 3x2 + 4x – 7. (find the vertex, intercepts and reflection)

12. Find the vertex by completing the square. f(x) = -3x2 + 6x + 8

13. The supply and demand curves are given for LeBron’s Shoes. Find the equilibrium price and the equilibrium quantity.

S(p) = 92p –1,000

D(p) = 20,000-74p