B
College Algebra
Unit 3.1-3.2 Exam
Name
Directions: Show all work and reasoning to receive full credit.
1) Rewrite the function 𝑓(𝑥) = −4𝑥 2 + 24𝑥 − 29 in the form f ( x)  a( x  h)2  k by completing the square
and determine the following:
a) vertex
b) x – intercepts (in radical form, no decimals)
c) y – intercept
2) Without completing the square, determine the following for the quadratic equation f ( x)  3x2  8x  3 .
(No decimals. Check your answer on the calculator.)
a) axis of symmetry
b) vertex
c) x-intercepts
d) y-intercept
B
3) Find an equation, in vertex form, for the parabola that has a vertex at (-5, 2) and a point at (-3, -1).
4) An engineer collects data showing the speed s of a given car model and its average miles per gallon M.
Speed, s
20
30
40
50
60
70
80
mpg, M
18
20
23
25
28
24
22
a) Use a graphing calculator to determine the quadratic function of best fit (round to the nearest thousandths).
b) Using the equation and graph from part (a) determine the speed of the car (to the nearest thousandths) that
will obtain the maximum miles per gallon.
5) The path of a diver is given byℎ(𝑥) = −4𝑥 2 + 16𝑥 + 12, where h is the height (in feet) and x is the
horizontal distance (in feet) from the end of the diving board. What is the maximum height of the diver?
(Show all work by hand. Check your answer on the calculator.)
B
6) A parabolic arch has a span of 280 feet and a maximum height of 65 feet.
a) Draw a diagram and determine the
b) Calculate the height of the arch at a point
equation for the parabola in vertex form.
60 feet from the center.
7) Let f ( x)  .02( x  5)( x  4)2 ( x  1)3
a) Determine the degree of the function.
b) Determine the end-behavior of the function.
c) Determine the y-intercept.
d) Determine the zeros and identify the multiplicity
of each.
e) Graph f using a graphing utility and
determine the local maxima and minima,
if any exist, rounded to two decimal places.
f) Graph the function by hand.
g) Determine the intervals on which f is
increasing and decreasing.
h) Determine the domain and range of f.
B
8) Form a polynomial, in standard form, whose zeros and degree are given.
Zeros: 0 multiplicity of 2;
-2 multiplicity of 2; 4 multiplicity of 1;
9) Determine the polynomial equation for the given graph.
degree 5