Mathematical Investigations III Poly Quiz
Sheets 1-8
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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
Vertex: Roots: y
 
2 x
2 
4 x
 

 y

3 y

2

3
 x
2 
2 x y

2

3
1 x
2 
2 x

1

2
1 ( x

1) y 2( x

1)
2 
5
2
0
 
2( x

1)
2  
( x

1)
2 

( x x
  
5
2
5
2
5
2
So Vertex = ( 1, 5)
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 ( )

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) ( x

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.
 x
 x
2 c.
d.
( )

3 x
3 
3
4 x
2 
3 g x
 x
3  x
2  
1 x
IMSA SP 12