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.