Polynomial Functions 3.1

Question 1

what are the steps to expand and simplify ex 4x(2x-5)(3x+2)

Answer 1

1. multiply out the brackets first (ex. foiling of distributing)
2. collect like terms to simplify

Question 2

factor

Answer 2

1. make sure x^2=1

2. decomposition

Question 3

transformations

Answer 3

a
-negative=reflection below x-axis
-positive=reflection above the y-axis
-greater than one, verticle stretch
-in between 1 and 0 vertical compression
k
-negative=reflection across y-axis
-horizontal stretch=k less than 1
-horizontal compression (shrink)=k greater than 
d
-horizontal translation
c
-vertical translation

Question 4

how to write a function equation from a graph parabola

Answer 4

1. Identify the vertex point
let's say you have the vertex point  (1,3)
2. plug it into a vertex form equation:
y=a(x-1)^2+3
3. then plug in a second point ex. (0,5)
5=a(0-1)^2+3
...
a=2
-solve from there to find a
4. write the full transformation equation by plugging in the needed info
y=2(x-1)+3
https://www.radfordmathematics.com/functions/quadratic-functions-parabola/vertex-form/vertex-form-finding-equation-parabola.html#:~:text=We%20can%20use%20the%20vertex,value%20of%20the%20coefficient%20a.

Question 5

What makes an expression a polynomial

Answer 5

An equation of variables and numbers with non negative exponents

• no variables in denominator of fraction
• no square roots

Question 6

What does a polynomial expression look like algebraically

Answer 6

Equations with variable exponents and coefficients

3x^3+12x^2+6x+4

Question 7

What is simplest polynomial?

Answer 7

Contains only a single term

Question 8

what are the characteristics of polynomial graphs?

Answer 8

-Polynomial of degree two of more than 2 does not have sharp-edged
-smooth and continuous
-no asymptotes
Domains and range are the set of real numbers

Question 9

what are the rules for a function to be a polynomial?

Answer 9

• no fractional powers
• no square roots
• no negative exponents
• no variables in the denominator

Question 10

What are finite differences

Answer 10

Differences between the output number in a table

• First differences is linear
• Second differences is quadratic
• Third differences are cubic

-only occurs if the differences are constant