Algebra homework

1.) Use the graph of f(x) to estimate the following.

WebAssign Plot 
 A.  Estimate the vertex.

(
x,
y) = ()   

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x <
−4
x >
−4
x <
−20
x >
−20

C. (c) For what x values is the graph decreasing? Write your answer as an inequality.

x >
−4
x < 4

 


D. (d) Estimate the x-intercepts. (If an answer does not exist, enter DNE.)

 

(x, y)  =  (smaller x-value)

 

(x, y)  = (larger x-value)

 

 

 

E. (e) Estimate the y-intercept. (x, y) =

 

F. (f) Estimate =  f(4).

 

2.)

Use the table to find the horizontal and vertical intercepts

Horizontal intercept (x,y) = ()  (smaller x-value)

Horizontal intercept (x,y) = () (larger x-value)

Vertical intercept     (x,y) = () 

Input | Output

-3      | 54

0       | 18

2       | 4

3       | 0

4       | -4

6       | 0

7       | 4

 

 

 


3.)

 

Refer to the given graph to answer the questions. Assume the function is written in the vertex form of a quadratic.

WebAssign Plot 

(a)Which point is the vertex?

(x, y) =

 

(b) What is the equation of the axis of symmetry?

(c) Would the value of a be positive or negative?

(d) In vertex form, what are the values of h and k?

h  =    

k  =    

(e) What is the symmetric point to the point (5, 4)?

(x, y) =

 

 


4.)

The total number of people, in thousands, who were below the poverty level can be modeled by

N(t) = 155(t − 9)2 + 33417  where N(t) represents the total number of people in the United States who were below the poverty level, in thousands, t years since 1990.†

(a) How many people were below the poverty level in 1999?

In 1999 there were about   thousand people below the poverty level in the United States.

(b) Find N(15) and explain its meaning.

In   there were about   thousand people below the poverty level in the United States.

(c) Sketch a graph of this model.

 

WebAssign Plot 

 

 

 

 

 

 

 

 

 

 

 

 

(d) Estimate the vertex of this model and explain its meaning.

According to this model, in   there were about   thousand people below the poverty level in the United States which is a  —Select— maximum minimum .

 

(e) Use your graph to estimate when the number of people in the United States below the poverty level was 43 million.

According to the graph, in about   and again in   the number of people in the United States below the poverty level was 43 million.

 

(f) If the domain for this model is [3, 18], find the range.

[33,417, 45,972]

[0, 33,417]    

[3, 18]

[0, ∞]

[31,500, 46,500]

 

 


5.)

Give the domain and range of the quadratic function.

g(x) = −0.25(x − 7)2 + 15

Domain:

[15, ∞)

(−∞, 7]    

[−15, ∞]

[7, ∞]

(−∞, ∞)

Range:

[7, ∞)

(−∞, −15]    

(−∞, ∞)

[15, ∞)

(−∞, 15]

 

 


6.)

Consider the following.

Input, X | Output, Y

1            |320

3            |180

5            |80

7            |20

9            |0

11          |20

 

Find an equation for a model of the given date.

Give the domain and range for the model you found. (Hint: This problem does not have a context, so the domain and range will not be restricted.)

Domain:

[1, 11]

[0, ∞)    

[0, 320]

(−∞, 20]

(−∞, ∞)

Range:

(−∞, 0]

[1, 11]

[0, ∞)

[0, 320]

(−∞, ∞)

 

 


7.)

The total number of people, in thousands, age 65 years old and over who were below the poverty level can be modeled by N(t) = −59(t − 12)2 + 3890

where N(t) represents the total number of people 65 years old and over in the United States who were below the poverty level, in thousands, t years since 1980.†

 

(a) How many people 65 years old and over were below the poverty level in 2000?

In 2000 there were   people 65 years old and over below the poverty level.

 

(b) When were there 1 million people 65 years old and over below the poverty level? (Hint: 1 million = 1000 thousand)

According to this model, there were 1 million people 65 years old and over below the poverty level in the years ___   (smaller value) and ____  (larger value).

 

(c) What is the vertex of this model, and what does it represent?

In about   there were   people 65 years old and over below the poverty level. This was the maximum number of people around this time.