College Algebra
Chapter 3 Take-Home Quiz
Name
Period:______
Due: Odds: Friday March 2nd
Evens: Monday March 5th
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), and y-intercept of the
following quadratic function by completing the square and writing it in vertex form.
f ( x)  3x2  12 x  1
2) Use the quadratic function g ( x)  16 x2  32 x  15 to:
a) Find the axis of symmetry.
b) Find the vertex.
c) Find the x- and y-intercepts.
20
3) Determine an equation in vertex form for the graph of the parabola.
18
16
14
12
10
8
6
4
2
-12 -10 -8 -6 -4 -2
-2
-4
4) Form a polynomial in standard form whose zeros and multiplicities are given.
Zeros: 3, multiplicity 2; 0, multiplicity 3; -2, multiplicity 2; degree 7
2 4 6 8 10 12
6) Let f ( x)  ( x  3)( x2  4)( x  6)3
a) Determine the degree of the function.
b) Determine the y-intercept.
c) Determine the zeros, identify the multiplicity of each and determine whether the graph crosses or touches at
each zero.
7) Accurately graph the following function by determining the following: f ( x) 
a) write f in lowest terms
3x 2  11x  4
2 x 2  5 x  12
b) x- and y-intercepts
1
1
c) vertical asymptote(s) and/or holes d) horizontal or oblique asymptote
e) additional points
8) Accurately graph the following function by determining the following: f ( x) 
a) write f in lowest terms
x3  x 2  12 x
x2  4
b) x- and y-intercepts
1
1
c) vertical asymptote(s) and/or holes
d) horizontal or oblique asymptote
e) additional points
9) Solve the following inequalities.
a) 4 x3  4 x  6 x 2
b)
12 x
 6x
4 x
10) Find all of the real zeros of the polynomial function.
f ( x)  4 x4  9 x3  3x2  18x 10
11) Use the given zeros to find the remaining zeros of the function.
f ( x)  3x4 19 x3  69 x2  99 x  26; zero: 2  3i
12) Find ALL zeros of the function.
g ( x)  x4  2 x3  5x2 18x  36