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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

Vertex: Roots:

*y*

2

*x*

2

4

*x y*

3

*y*

2

3

*x*

2

2

*x*

*y*

2

3

*x*

2

2

*y*

2(

*x x*

1)

2

2

1)

2

5

*x*

1

0

2(

*x*

1)

2

(

(

*x x x*

1)

2

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

IMSA

2

*x*

2

*bx*

4 . Find all values of

*b*

such that if the roots of this quadratic are complex.

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.

2(

*x*

3)(

*x*

3)

2 b.

6. Label each as a polynomial (p) or not a polynomial (n): a.

*x*

3

3

*x*

2

4 b.

*x*

*x*

2 c.

3

*x*

3

3

4

*x*

2

3 d.

*x*

3

*x*

2

1

*x*

IMSA

2(

*x*

*x*

*x*

3)

SP 12