Mathematical Investigations III
Poly Quiz
Sheets 1-8
Name __________________
No Calculator.
Show your work to receive full credit:
1 a. Complete the square on the following and give the vertex and zeroes of the parabola. Show your
work.
y  2 x 2  12 x  5
Sketch the parabola y  2 x 2  12 x  5 below. Clearly indicate significant points
and describe how they relate to the above problem in 1a.
b.
y
8
x
-8
-8
8
2. Given f ( x)  ax 2  bx  c . Explain how you can determine if the roots of this quadratic are complex
or realm without solving for the roots.
IMSA
SP 12
3. Write an equation (if possible) for the polynomial function which meets the following criteria:
a. cubic, a single root of multiplicity one at x = 5 and no other x-intercepts.
b. fourth degree with three real roots.
c. a fifth degree polynomial with a bounce point at x = 3, a pass through point at x  2 , and no
other x-intercepts.
4. All even degree polynomials are even functions. True or False? Explain.
5. Sketch the graph of each polynomial. Label all intercepts.
a. 2( x  3)( x  3) 2
b. ( x  1)3 ( x  2)2 (2  x)
6. Label each as a polynomial (p) or not a polynomial (n):
a.
f ( x)  x 3  3 x 2  4
b. g ( x)  x  x 2
3
c. h( x)  3x3  x 2  3
4
1
d. g ( x)  x 3  x 2  x 
x
IMSA
SP 12