IA3 Jeopardy #2

IA1/IA2

100

Graph: y = 2x - 5 

y = -2/3x + 3

SEE GRAPH

200

Find the point of intersection: 

y = 2x - 5 

y = -2/3x + 3

x = 3

y = 1

(3, 1)

300

Solve: 

1/3x - 2 < -1/3x + 4

x < 9

400

What is the equation of a line that goes through the points...

(-2, 11) and (1,2)?

y = -3x + 5

500

Graph: 6y - 4x = -24 

Find the x and y-intercepts

SEE Graph 

y = 2/3x - 4 

Y-Intercept: (0,-4)

X-Intercept: (6,0)

OER

100

Solve for x: 

100x² + 36 = D

See answer on board

+/- √(D – 36)/10

200

x = time (days)

y = height (inches)

2 points: (10,6) and (30,18). 

Find the equation of the line going through the two points. What is the expected height on day 65?

y = 3/5x

x = 65       y = 3/5x

y = 3/5(65)

Height = 39 inches

300

Cost function: C = (8/3)x + 20

Revenue Function: R = 5x - 1

x = # of days. Graph both functions. When does cost = revenue?

9 days ($44) 

(8/3)x + 20 = 5x - 1

400

Graph: y = (x-2)² - 9

SEE GRAPH

Vertex: (2, -9)

X-Intercepts: (-1,0) and (5,0)

Y-Intercept: (0, -5)

500

A rectangle has an area of 160 m². The length of the rectangle is 6 meters longer than the width. What is the width? What is the length?

x(x+6) = 160

Width = 10 m

Length = 16 m

Quadratics

100

Factor: x² - 17x + 30

(x - 15) (x - 2)

200

Solve: x² - 17x + 30

x = 15

x = 2

300

Factor and Solve: 2x² -11x + 15

(2x - 5)(x - 3)

x = 5/2

x = 3

400

What are the sum of the roots of...

2x² - 11x + 15

x = 5/2

x = 3

5/2 + 3 = 11/2

ANSWER: 11/2 or 5.5

500

Solve by completing the square:

x² - 4x - 12 = 0

x = 6

x = -2

Functions

100

f(x) = 2x² - 10

g(x) = 7x + 4

Find f(3) 

Find g(3)

f(3) = 8

g(3) = 25

200

Find the vertex: y = x² + 10x + 16

(-5, -9)

300

Consider the function x² + bx - 10, where b is a constant. If the function has an axis of symmetry of x = 7, what's the value of b?

b = -14 

400

f(x) = 2x² - 10

g(x) = 7x + 4 

For what value, is f(x)>g(x)

a) x = 2

b) x = 3

c) x = 4

d) x = 5

d) x = 5

f(5) = 40

g(5) = 39

500

Nylah's profit, r(x) for selling x video games is represented by the function r(x) = -20x² + 80x + 100. What is the domain of the function?

a) All real numbers

b) All integers

c) All whole numbers

d) All positive real numbers

x = domain = # of video games

Video games CANNOT be negative, CANNOT be a fraction, CAN be zero

ANSWER: c) All whole numbers

Miscellaneous

100

What special case quadratic is a⁴ - b⁴

Difference of Squares

200

Factor: a⁴ - b⁴

(a² - b²)(a² + b²)

OR 

(a - b)(a + b)(a² + b²)

300

Are the following points representative of a function? Why? 

(-2,9)

(1,7)

(3,4)

(-2, 11)

No because an input (x = -2) has more than output, or an x-value repeats. So, it is not a function

400

At what point do the lines y = 4x - 14 and y = 8x - 26 intersect?

4x - 14 = 8x - 26

x = 3

y = -2 

(3, -2)

500

Choose the expressions that are equivalent to x² + 6x + 5. Choose all that apply

a) (x + 3)² + 4

b) (x + 3)² - 4

c) (x + 3) (x + 2)

d) (x + 5) (x + 1)

e) (x - 5) (x - 1)

b) (x + 3)² - 4

AND

d) (x + 5) (x + 1)