3.5: Finding Real Roots
3.6: FTA
3.7: Investigating Graphs
3.8: Transforming Graphs
3.9: Modeling with Polynomials
100
Solve by factoring:
x^4-12x^2+36=0
x=6, x=-6
100
Write the simplest polynomial given the following roots: -4, -1, 2
x^3+3x^2-6x-8
100
What is the end behavior of the following function?:
f(x)=2x^5-x^2+75
As
x -> oo, f(x) -> oo
As
x -> -oo , f(x) -> -oo
100
If g(x)=x^4-6 , then find g(x)-4 and describe the transformation using words
g(x)-4=(x^4-6)-4=x^4-10
Vertical shift down 4 units.
100
Determine the type of function that best fits the data:
Cubic!
200
Solve by Factoring:
10x^3-640x=0
x=0, x=8, x=-8
200
BONUS QUESTION: How much does guacamole cost at Chipotle? (Within 50 cents)
$2.70!!
200
What is the end behavior of the following function?
f(x)=-331x^44+98
As
x -> oo , f(x) -> -oo
As
x -> -oo , f(x) -> oo
200
If j(x)=3x^4+8 , find j(x-8) and describe the transformation using words
j(x-8)=3(x-8)^4+8
Horizontal shift right by 8 units.
200
Determine the type of function that fits the data:
Quartic!
300
Solve by factoring:
2x^3-5x^2-4x+10=0
x=+-sqrt2, x= 5/2
300
Write the simplest polynomial given the zeros:
3i, sqrt2
x^4+7x^2-18
300
Identify whether the graph has a positive or negative leading coefficient and an even or odd degree:
Negative LC, odd degree
300
Reflect h(x)=3x^3-4x^2-2x+7 across the x-axis.
-h(x)=-3x^3+4x^2+2x-7
300
A bank is trying a new program for their high yield savings accounts, where x represents years and y represents dollars. Find the function the bank is using for their new program:
f(x)=16x^2-24x
400
Identify the roots of the equation and state their multiplicities:
8x^5-192x^4+1536x^3-4096x^2
x=0; 2, x=8; 3
400
Solve the equation by finding all roots:
x^4+5x^2-36=0
x=+-3i, x=+-2
400
Tell whether the function has a positive or negative leading coefficient and an even or odd degree:
Positive LC, even degree
400
Given q(x)=3x^5-7x^2 , find 3q(x)
3q(x)=3(3x^5-7x^2)=15x^5-21x^2
400
BONUS QUESTION: Within 5 years, what was the last year the Detroit Tigers won the World Series
1984
500
Identify the roots of the equation. State their multiplicities.
x^4+2x^3-11x^2-12+36=0
x=-3; 2, x=2; 2
500
Solve the equation by finding the roots:
x^4-3x^3+5x^2-27x-36=0
x=-1, x=4, x= +-3i
500
Graph the function without using a graphing calculator:
g(x)=25x^2-4
500
If v(x)=2x^4-6x^3+3x^2-x+7 , find v(-x) and describe the transformation using words
v(-x)=2x^4+6x^3+3x^2+x+7
Reflection across the y-axis
500
Using only a traditional graphing calculator, find the function that fits the data:
f(x)=4x^4-32x^2+4