Download poly practice test 4 f14

Practice test 4
Name________________
1.
2.
Polynomials are ________ and _________.
If an equation with a degree of 7 has a negative leading coefficient, the end behavior notation isWrite an equation of least
degree (in factored form) of a polynomial has the following zeros: 0,5, i
3.
Sketch a quartic with 2 real zeros, maximum number of turns and a positive leading coefficient.
4.
5.
If a polynomial has a degree of 6, then it will have ____ total complex roots (real and imaginary combined).
If a polynomial has a degree of 5, then it can have up to a maximum of ___ turns in its graph.
6.
7.
8.
9.
If 5i is a root of a function then what other value also must be a root of that function? ________
When a root is repeated 2 times, it is commonly stated that the root has a _____ of 2.
Polynomials can not have vertical asymptotes because they are _____________________.
Polynomials can not have exactly one imaginary root because
________________________________________________________________________.
10.
( x − 7) 2 ≠ x 2 + 49 because
___________________________________________________________________________.
11. Both ends of a graph go in the same direction if the polynomial has an ___________ degree.
12. If the leading coefficient of a polynomial is negative the right side will __________________.
13.
The complex conjugate of 9 − 7i is _____________.
14.
The absolute value of
15.
− 5 + 12i = − 5 + 12i which equals ___________.
y = x( x + 3) 2 ( x + 10)( x − 1) has a degree of ______
16. The polynomial above has the following real zeros:
17. The graph of the polynomial in #16 will cross the x-axis at all real zeros except at _______, where it will just touch the x-axis
and then bounce back to the same side.
18. Fill in the chart by sketching the correct end behavior. Then complete the notation for each end.
Degree Even
Degree Even
Degree odd
Degree odd
LC positive
LC negative
LC positive
LC negative
Left notation
Right
notation
Left notation
Right
notation
Left notation
Right
notation
Left notation
Right
notation
1.
Sketch a cubic function with the maximum number of turns and 3 real roots with a negative leading coefficient.
2.
Sketch a quadratic function with a maximum number of turns, only 2 real roots and a positive leading coefficient.
3.
List the degree and leading coefficient. Then circle the correct description
y = 10 x 2 + 2 x 6 + 2
degree #______even or odd
leading coefficient #_____ positive or negative
y = −2 x 7 + 5 x 4 + 1
degree #______even or odd
leading coefficient #_____ positive or negative
y = −12 x 4 + 7 + 6 x 5 degree #______even or odd
leading coefficient #_____ positive or negative
th
4. Sketch a 6 degree polynomial with a positive leading coefficient and the maximum number of turns. Show only 2 real
zeros.
5.
The MAXIMUM number of turns a polynomial function can have is determined by using the following formula:
degree minus __________
6.
A 9 degree polynomial could have up to ___ turns.
7.
Look at the graph below. Does it have any absolute maximum or minimum points?
th
:
8.
Another name for global maximum is _____________ maximum
9.
Another name for local maximum is ______________ maximum
Explain.
Mark on the graph all the points that are maximums or
minimums. Indicate on each one if they are local or global.
10. List the degree number and parity of the following types of polynomial functions and write an example equation for each.
Type of polynomial
Degree number
Degree Parity
(even or odd)
Example equation
Constant
Quintic
Quadratic
Linear
Quartic
Cubic
11. For each set, write an equation of least degree in factored form of a polynomial has the following roots
Given the following zeros: { -12, 1, 2i}
Given the following zeros: {-8,0,3}
Given the following zeros: { -3 multiplicity of 2}
From previous tests especially review factoring and solving!
Solve each quadratic. Write your answers in a solution set. Use any method, but show your work for full
credit. If your work is on scratch paper, be neat and clearly label.x
0 = x 2 − 16
y = x 2 − 17
y = ( x + 3)( x − 1)
y = x 2 − 13 x + 40
y = ( 2 x + 1)( x + 9)
− 3 x = 2 x 2 − 7 x + 13
y = x2 − 5x
y = ( x − 4) 2 + 6
5 = x2
For the following expressions, FACTOR ONLY
x 2 − 25
8 x 2 − 200
x 2 − 23 x + 42
x 2 − x − 20
3 x 2 + 11x − 4
40 x 2 + 8 xr 2 − 15 x − 3r 2
Find the discriminant and state the nature of the roots (do not solve)
0 = x 2 + 6 x + 10
Write an example of an equation that is NOT a polynomial and explain why.
What is the vertex of these quadratics?
1
y = ( x + 5) 2 − 1
3
y = ( x + 5)( x + 1)
y = x2 + 6x − 3
Complex number practice
Simplify each and write in proper form
6
i
3 − 7i
7 + 4i
i 81
i 43
i + 5i − i 2
− 7 − 2i
(i )
3 4