Chapter 2 Jeopardy

Linear Functions

100

Determine the y-intercept and slope of f:

f(x)=(8/9)(x)-4

y-intercept: -4 

Slope: 8/9

200

Find the average rate of change of f on the interval [0,3] where f(x)=-2x+15.

-2

300

If f is a linear function where f(-2)=1 and f(4)=13, find the formula for f(x).

m=2, y-intercept=5

f(x)=2x+5

400

Find an equation of the line perpendicular to the graph of f(x)=2x+5 and passing through the point (4,-1).

m=-1/2, y-(-1)=(1/2)(x-4)

y=(-1/2)x+1

500

A delivery company purchases a new delivery van for $12,000. The company estimates that after 5 years, the van will have a value of $2,000. Assume the value of the van depreciates linearly. 

What is the value of the van after 3 years?

V(t)=12,000-2,000t

V(3)=12,000-2,000(3)= $6,000 

Quadratic Functions

100

Use the square root property: (5x-2)²+9=0

x=(2+3i)/5, (2-3i)/5

200

Use factoring: x²+7x+10=0

x=-2,-5

300

Use completing the square: 3x²-18x+6=0

x=3+sqrt(7), 3-sqrt(7)

400

Use the quadratic formula: 3x²-4x+5=0

x=(2+i sqrt(11))/3, (2-i sqrt(11))/3

500

Use any method: 2x²+5x=1

x=(-5+sqrt(33))/4, (-5-sqrt(33))/4

Quadratic Functions II

100

Find the vertex of f(x)=-3x²+12x-5.

f(2)=7

200

Does f(x)=-3x²+12x-5 have a maximum or minimum and what is it?

Maximum value of 7 at x=2.

300

Sketch the graph of f(x)=-3x²+12x-5. 

I'll determine if correct. 

400

A tennis player hits a high lob from an initial height of 4 feet above the court. The ball goes straight up into the air, and its height (in feet) after t seconds is given by

h(t)=-16t²+64t+4.

What is the height after 1 second?

52 feet

500

A tennis player hits a high lob from an initial height of 4 feet above the court. The ball goes straight up into the air, and its height (in feet) after t seconds is given by

h(t)=-16t²+64t+4.

How long does it take for the ball to reach its maximum height?

2 seconds

Absolute Value Functions

100

Solve for |x-5|=7

x=12 and x=-2

200

Solve for 5-|x-2|=2

x=5 and x=-1

300

Solve for 3|(x-4)/3|=5

x=9 and x=-1

400

Solve for |x-2|+5=9

x=6 and x=-2

500

Solve for |3x+5|=|2-4x|

x=-3/7 and x=7

Linear and Absolute Value Inequalities

100

Solve and express your answer using interval notation:

-3x+4>2x-6

(-infinity,2)

200

Solve and express your answer using interval notation:

-2-3x (less than or equal to) 4-x < 10-2x

[-3,6)

300

Solve and express your answer using interval notation:

-3x+2 (greater than or equal to) 11 

or 4x-5 (less than or equal to) -17

(-infinity,-3]

400

Solve and express your answer using interval notation:

|2x-7| (greater than or equal to) 7

(-infinity, 3] U [4, infinity)

500

Solve and express your answer using interval notation:

|2x-3|>11

(-infinity,-4) U (7, infinity)