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.
Vertex:
Roots:
13
y 5
0  2( x  3) 2  13  ( x  3) 2 
y  2 x 2  12 x  5 
 x2  6x
2
2
13
y 5
 ( x  3)  

 9  x2  6 x  9
2
2
y 5
13

 9  ( x  3) 2
 x  3
2
2
2
 y  2( x  3)  13
So Vertex = (3, 13)
b.
Sketch the parabola y  2 x 2  12 x  5 below. Clearly indicate significant points . Label the
scales on both axes. Neatness and accuracy count
.
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.
We look at b 2  4ac . If this quantity, called the discriminant, is negative the roots 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.
y  ( x  5)( x 2  1)
b. fourth degree with three real roots.
y  ( x  5)2 ( x  1)( x  3)
c. a fifth degree polynomial with a bounce point at x = 3, a pass through point at x  2 , and no
other x-intercepts.
y  ( x  3)2 ( x  2)3 or perhaps y  ( x  3)2 ( x  2)( x 2  1)
4. All even degree polynomials are even functions. True or False? Explain.
This is false. For example, f ( x)  x 2  x has degree 2 which is an even degree, but this function is not
even. f ( x)  ( x)2  ( x)  x 2  x  f ( x)
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