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  4 x  3
b.
Sketch the parabola y  2 x 2  4 x  3 below. Clearly indicate significant points. Label the
scales on both axes. Neatness and accuracy count.
2. Given f ( x)  2 x 2  bx  4 . Find all values of b such that if the roots of this quadratic are complex.
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 one root of multiplicity 3 and no other real roots.
c. a fifth degree polynomial with a bounce point at x = 2, a pass through point at x  1 , and no
other x-intercepts.
4. Label each graph of a polynomial as having even degree (E) or odd degree (O). If the graph cannot
be a polynomial label (N).
5. Sketch the graph of each polynomial. Label all intercepts.
a.
f ( x)  2( x  3)( x  3)2
b. g ( x)  2( x  1)3 ( x  2)2 ( x  3)
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