Pre-Calculus
Unit 2
2.1 – 2.2 Practice Problems
DUE: Today (End of period)
Name____________________________________
Part I: Non-Calculator Problems
You should be able to do the following without a calculator.
A
B
C
D
E
F
G
H
1) True or False: Mark each statement as true or false. If false provide a counterexample
in the third column.
Statement
TRUE/FALSE
Counterexample/reason
All linear functions have both and x- and yintercept.
All quadratic functions have a y-intercept.
All quadratic functions have an x-intercept
.
Any constant function and any linear
function will have graphs that intersect.
Any constant function and any quadratic
function will have graphs that intersect.
The function f ( x)  3( x  2) 2  5 has a
vertex of (2, 5).
The function f ( x)  3( x)2  5 has two xintercepts.
The function f ( x)  3( x  2)( x  8) has and
axis of symmetry of x  5 ,
2. For the function f ( x)  x3  4 x 2  5x ,
a. Find all zeros of f.
Zeros of f:_______________________
3. Launching a Rock Larry uses a slingshot to launch a rock straight up from a point 6 ft above
ground level with an initial velocity of 160 ft/sec.
a. Find an equation that models the height of the rock t seconds after it is launched.
Equation:________________________________
b. What is the maximum height of the rock? When will it reach that height? Show your work.
(Yes, you can do this without a calculator!)
Maximum height:___________
Time to reach maximum height:__________
c. Explain to someone who is new to Pre-Calculus how you could find when the rock hit the
ground. Answer in complete sentences.
4. Let f ( x)  ( x  a)( x  b)2 ( x  c)3 , such that a, b, and c are real numbers.
5a. What is the degree of f(x)? ____________
5b. How many non-real zeros does f have?____________
5c. What are the x-intercepts of f?____________________________
5d. Evaluate the limits:
lim f ( x)  _____
x
and
lim f ( x)  _____
x
5. Find the vertex and axis of the graph of the function f ( x)  2 x 2  16 x  31 . Show your work!
6. Write an equation for the quadratic function in vertex form whose graph contains the given
vertex and point. Show your work!
Vertex (-2, -3), point (1, 2)
Equation:_____________________________________
7. Find all of the real zeros of the function, finding exact values whenever possible. State the
number of non-real zeros. (Hint: Use factoring for both).
a. f ( x)  x 4  10 x3  21x 2
b.
Zeros:________________________
Zeros:__________________________
Part II: Calculator Problems You may use a graphing calculator for these problems. Round all
decimal values to three places.
14. Volume of a Box Villareal Paper Co. has contracted to manufacture a box with no top that is
to be made by removing squares of width x from the corners of a 30-in. by 70-in. piece of
carboard.
a. Find an equation that models the volume of the box. _________________________________
b. Determine x so that the box has a volume of 5800 in3. Round to 3 decimal places.
x = ______________
c. (Not in the book) Determine x so that the box a maximum volume .
Answer: _________________________
15. The Perry family wants to install a moat of uniform width around their rectangular castle.
The dimensions of their castle are 100 ft by 150 ft. If the area of their land (including both castle
and moat) is 23,400 ft2, find the width of the moat.
Width of moat:_______________________
Reflection: Were you able to complete these on your own? Where you honest about not using a
calculator on the non-calc pages? If your answer was NO to either of the first two questions
what specific actions will you take to make sure you are ready for independent assessments?
What questions do you still have about: definition of polynomials, constant, linear and/or
quadratic functions? How will you get the answers?