Mathpardy - 124 Exam 2 Review

Quadratics

100

Factor:
x²+5x+6

(x+2)(x+3)

200

Solve:

x²-4x-12=0

x=6,-2

300

Find the Vertex coordinate:
f(x)=3x²-12x+11

(2,-1)

400

Solve:
(x+2)(x-3)=-4

x=-1,2

500

Write in standard form:
3x²-12x+11

3(x-2)²-1

Applications

100

Given h(t)=-16t²+42t represents the height (in feet) of a projectile launched after t seconds.
What was the initial height of the projectile?

0ft

200

C(x)=(2x-5)^1/2 represents the number of gallons of milk consumed by the average American household each month, given the number of people in the household, x.

How many gallons are used each month in a house with 5 people in it?

2.2 gallons

300

The volume of a box with a square base is given by
V(x)=x³+8x²+16x, where x represents the height (in inches) of the box. 

How much volume (in³) would a box that is 2ft tall hold?

18,816in³

400

Given h(t)=-16t²+42t represents the height (in feet) of a projectile launched after t seconds.

What is the maximum height of the projectile?

27.6ft

500

An arrow that is fired up in the air follows the model:
A(t)=-16t²+308t+22 where A(t) represents the height of the arrow after t seconds.

When does the arrow reach a height of 10ft?

19.289seconds

Exponents

100

Simplify
(3xy²)⁰

1

200

Simplify
(2x)²(2x)³

32x⁵

300

Solve:
2(3+x)⁴=32

-1

400

(2x^-1x³)^-2(x¹x^-5)^-1

1/4

500

(32x¹⁰)^2/5(8x¹²)^-1/3

2

Polynomials

100

State the degree and leading coefficient:
4x³-2x²-x⁶+4

degree: 6, lead coeff: -1

200

Is the following a polynomial (yes/no)?
3x²-6x-4x⁵-3x^-1

No

300

If a polynomial graph has 6 turning points and 3 x-intercepts, with ends going in opposite direction, what possible degree could it be?

7

400

Find the relative maximum value of the function:
V(x)=x(8-x)(10-x)

105.028

500

Is the following a polynomial? If not, why? If so, what is it's degree and leading coefficient?

f(x)=2

Yes, it is a constant polynomial and has a degree of 0 (zero) with a leading coefficient of 2.
f(x)=2x⁰

Business

100

C(x)=13x+4800
R(x)=35x
P(x)=22x-4800

How much profit does the business make if they produce and sell 250items?

$700

200

C(x)=13x+4800
R(x)=35x
P(x)=22x-4800

How many items must be sold to break even?

218.2 items (218 items realistically)

300

C(x)=13x+4800
R(x)=-0.2x²+140x
P(x)=-0.2x²+127x-4800

How many items should be sold to make $20,000 in revenue?

200 items or 500 items

400

C(x)=13x+4800
R(x)=-0.2x²+140x
P(x)=-0.2x²+127x-4800

What is the company's maximum profit?

$15,361.25

500

C(x)=13x+4800
R(x)=-0.2x²+140x
P(x)=-0.2x²+127x-4800

How many items must be sold for the company's revenue to overcome their costs?

40 items or 595 items