College Algebra
Unit 3a Study Guide (3.1 – 3.2)
Name
Directions: Show all work and reasoning to receive full credit. All problems must be done analytically,
unless specified otherwise.
1) Algebraically determine the axis of symmetry, vertex, x-intercepts (in radical form, no decimals), y-intercept,
domain, and range of the following quadratic function by completing the square and writing it in transformation
form.
f ( x)  2 x 2  10 x  3
2) Use the quadratic function g ( x)  16 x2  32 x  15 to:
a) Find the axis of symmetry.
c) Find the x- and y-intercepts.
b) Find the vertex
3) Determine an equation in transformation form for the graph of the parabola.
Write the equation in standard form.
20
(-1, 17)
18
16
14
12
10
8
6
4
(7, 1)
2
-12 -10 -8 -6 -4 -2
-2
-4
2 4 6 8 10 12
4) The following table shows the median number of hours of leisure time that Americans had each week in
various years.
Year
Median # of Leisure hrs per Week
1973
26.2
1980
19.2
1987
16.6
1993
18.8
1997
19.5
a) Use x = 0 to represent the year 1973. Using a graphing utility, determine the quadratic regression
equation for the data given (round to the nearest thousandths).
b) Using a graphing utility and the quadratic equation found in part (a), predict the year that Americans had
the least time to spend on leisure.
5) A suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road
surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the
road surface at the center of the bridge. Illustrate this scenario on a coordinate plane and find the height of the
cable at a point 200 feet from the center of the bridge.
6) A projectile is fired from a cliff 300 feet above the water and an inclination of 45o to the horizontal, with a
muzzle velocity of 250 feet per second. The height h of the projectile above the water is given by
32 x 2
h( x ) 
 x  300 , where x is the horizontal distance of the projectile from the base of the cliff. How far
(250)2
from the base of the cliff is the height of the projectile a maximum and what is this maximum height? (Show
work!! Check your answer on the calculator.)
7) For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches
the x-axis at each x-intercept and state the end behavior.
f ( x )   x 2 ( x  3)3 ( x  7) 4
8) Form a polynomial whose zeros and degrees are given.
Zeros: 3, multiplicity 2; 0, multiplicity 3; -2, multiplicity 2
9) Analyze the graph of the given function f as follows: f ( x)  ( x  3)( x2  4)( x  6)3
a) Determine the degree of the function.
b) Determine the end behavior.
c) Find the x- and y- intercepts of the graph.
d) Identify the multiplicity of each zero and state whether it crosses or touches the x-axis.
e) Graph f using a graphing utility and determine the local maxima and local minima, if any exist (round
to nearest thousandths).
f) Determine the domain and range.
g) Determine the intervals on which the graph of f is increasing and decreasing.