Business Math Graphing, Factoring, and Functions

Linear/Quadratic Equations

100

2x+5. Solve for X

x=-2.5

200

x²-25. Solve for X

(x+5)(x-5)

x=-5,5

300

using points (1, 15) and (2, 18), find your y=mx+b equation and solve for x.

x=4

400

3x²+11x+6=0, Solve using the AC method. Leave your answer as a fraction if you get one.

(3x+2)(x+3)

x=-3,-2/3

500

2x²-5x+3 using the quadratic formula, find x.

x=3/2, x=1

Slope/Sketch the Graph

100

Using the points (4,2) and (7, 5), find the slope intercept equation.

y -= x - 2

200

f(x)= 1/2x - 2

https://www.desmos.com/calculator/pdzkfnttfp

300

use (2,1) and (3,-1) to find your slope and graph.

y=-2x +5

https://www.desmos.com/calculator/wd8behomit

400

Vertex: (0,-25) X Intercepts: (-5, 0) and (5, 0) Sketch the Graph.

y=x^2 - 25

https://www.desmos.com/calculator/vqk8a3jtiz

500

y=(x-2)^2 + 1

Vertex: (2,1)

https://www.desmos.com/calculator/822s7ezqcz

Functions

100

For f(x) = 2x^3, would f(-3) equal a positive or negative number?

Negative

200

if f(x) = 2x^2 + 12x - 22

find f(q).

f(q) = 2q^2 + 12q - 22

300

If f(x) = x^2 + 2x +1,

Find f(5)

f(5) = 36

400

If f(x) = x^2 + 2x +1,

find f(10 + 2)

169

500

  if f(x) = x^2 + 2x + 1 and g(x) = 3x + 5, what is the value of f(1) - g(3) ?

3

Recognizing Functions and Factoring

100

Is the following set of ordered pairs a function?

{(10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9)}

Yes.

200

Factor completely. b² + 8b + 7 

(b+7)(b+1)

300

Solve for x by factoring. n² − 11n + 10 

n = 10, 1

400

Factor completely. 3p² − 2p − 5 

(3p - 5)(p + 1)

500

Solve for X using factoring. 2v² + 11v + 5 

v = -1/2, -5

Word Problems

100

Flip's Toy Factory records a marginal cost of $14 per bear and a fixed cost of $700. Write out the cost function, c(x).

C(x)= 14x + 700

200

Find the average cost of 400 books, if it costs $60 per book plus a flat rate of $360.

average cost = c(x)/x

average cost = c(x)/x = $60.90

300

The cost of renting tuxes for the Choral Society's formal is $20 down, plus $86 per tux. Express the cost C as a function of x, the number of tuxedos rented.

a) What is the cost of renting 5 tuxes?

b) What is the cost of the 5th tux?

C(x)= 86x + 20

a) C(5)=450

b) The cost of the 5th tux is $86. 

400

A soft-drink manufacturer can produce 1000 cases of soda in a week at a total cost of $6000, and 1500 cases of soda at a total cost of $8500. Find the manufacturer’s weekly fixed costs and marginal cost per case of soda. (hint: ordered pairs + the equation to find slope)

c(x) = 5x+ 1000

500

Your college newspaper, The Collegiate Investigator, has fixed production costs of $70 per edition, and marginal printing and distribution costs of 40¢/copy. The Collegiate Investigator sells for 50¢/copy. 

a)Write down the associated cost, revenue, and profit functions. (200 points)

b) What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator? (300 points)

c) How many copies should be sold in order to break even? (extra 100 points)

a) C(x)=0.40x + 70, R(x)= 0.50x, P(x)=0.10x-70

b) P(500)= -20

c) x=700