Algebra 2 – Segment One Exam Review

1. Given the two points )4,2( and )10,1( answer the following:

a. Write the equation of the line in point-slope form.

b. Convert the point-slope equation found in (a) to slope-intercept form and explain the

process using complete sentences.

c. Convert the slope-intercept equation found in (b) to standard form and explain the

process using complete sentences.

2. Graph the following linear equation,

and provide the slope and y-

intercept.

124 yx

Slope_____________

Y-intercept___________

3. Graph the following linear inequality.

12 xy

What type of line did you use and why?

How did you determine the direction to

shade?

4. Solve the following equation 35153 yy

5. Find )4(1f when 4

83)(

xxf

6. Describe what the graph of each situation would look like. Be sure to provide key

features of the graph in your explanation.

a. A flat charge of $12.

b. An initial fee of $10 and an additional charge of $2 per day.

c. A charge of $0.50 per day with no initial fee.

7. Convert each Rational Exponent to a Radical Expression.

a. 3

4

x b. 5

1

x c. 7

2

x

8. Simplify each using the properties of radical exponents.

a. 4

53

4

xx b.

5

2

7

6

x

x

c. 52 xxx

9. Solve each radical equation and check your answers.

a. 6372 x b. xx 15

10. How would you explain to your friend what an extraneous solution is?

11. Simplify each.

a. )38)(67( ii b. 2)51( i

12. How are the following problems different in their simplifying process?

)23)(2( xx

)23)(2( ii

13. Simplify each.

a. i

i

62

5

b. i63

4

14. A polynomial in descending order is written with the terms arranged from ____________

to ____________ degree.

15. Name each polynomial by degree and number of terms.

a. 24 810 xx b. 9103 23 nnn

16. Simplify each.

a. xxxx 435 44 b. 232 nn

c. 6353 xx d. xxxx 64822

17. Factor each completely.

a. 273 2 x b. 32162 2 xx c. 643 x

d. 34912 23 aaa e. 15652 23 ppp

18. Graph the quadratic and provide the key features of the graph.

6)3()( 2 xxf

Vertex____________

Axis of symmetry____________

Domain____________

Range____________

19. On the same coordinate plane from #18, graph the parabola

6)3(2)( 2 xxf and explain the differences in the graph using key features

of the graph.

20. Complete the square to solve the quadratic.

a. 026122 xx b. 01262 xx

21. Solve each quadratic using the quadratic formula.

a. 568 2 aa b. 2132 2 xx

20. Using what you know about the directix and focus, find the equation of the parabola

that will be equidistant from the fishing line (the focus) and the path of the fish (the

directix).

21. Using long division determine whether 5x is a factor of the function

253)( 23 xxxf .

22. What does the Factor Theorem tell you about #21?

23. Using synthetic division determine whether 2x is a factor of the function

10962)( 23 xxxxf .

24. What does the Factor Theorem tell you about #23?

25. Using the Rational Root Theorem and Descartes’ Rule of Signs, determine the zeros of

213892)( 23 xxxxf .

26. Describe the effects that “c” has on a given function f(x) in the following situtaions:

a. )( cxf

b. cxf )(

c. )(cxf

d. )(xfc

27. Without graphing technology describe how you would sketch a graph of

213892)( 23 xxxxf (from #25).

28. Multiply or Divide each and simplify. Be sure to list any restrictions.

a. 23 355

369

5

82

xx

x

x

x

b.

4014

90

9

162

22

xx

xx

x

x

29. Add or subtract each and simplify.

a. 2

2

1

4

xx b.

8

7

40355

552

n

n

nn

n

30. Simplify each complex fraction completely.

a.

1222

1184

5516

2

2

xx

xx

xx

b.

25

16

5

161

16

m

31. Find the oblique asymptote of 2

124)(

2

x

xxxf and explain the process.

32. Given the function 23

12102)(

2

2

xx

xxxf find each of the following discontinuities:

Vertical Asymptote____________

Holes____________

Horizontal Asymptote__________

33. Belle’s garden hose can fill the pool in 11 hours. Dempsey’s garden hose can fill the

pool in 14 hours. How long will it take to fill the pool using both hoses?

34. If you have 3 individuals who can do the same job at different times, write an equation

that can help you determine how long it will take them to complete the job together.

Explain your reasoning.