Basic Polynomial Opperations
(3x2+4x-3)-(x2-x+7)
2x2+5x-10
What does the leading term tell you about the graph of a polynomial function?
End Bahavior
What does an even multiplicity of a factor mean?
The function has a turning point at that x-intercept
Find x3-3x2+3x-1 divided by x-1
x2-2x+1
What transformations can we identify for polynomial functions in the form f(x)=a(x-h)3+k or f(x)=a(x-h)4+k
Vertical Strech/Compressions
Translations
Reflections
(3x+4)(x+5)
3x2+19x+20
What is the end behavior of f(x)=3x3+2x2-17x+1783?
as x->-infinity, f(x)->-infinity
as x->infinity, f(x)->infinity
What does an odd multiplicity of a factor mean?
The function crosses the x-axis at that x-intercept
Find 3x4-9x3+x2+4x-21 divided by x-3
3x3+x+7
What are the transformations from the parent function resulting in f(x)=2x3+17?
Vertical Stretch by a factor of 2
Translation up by 17 units
(2x+1)(x2+3x-1)
2x3+7x2+x-1
What is the end behavior of f(x)=-2x4+11x3+15x2-73.21586x+7.69821896333221?
as x->-infinity, f(x)->-infinity
as x->infinity, f(x)->-infinity
What is the behavior of the graph at each zero of f(x)=(x-2)4(x+11)2 ?
at x=2, f(x) has a turning point
at x=-11, f(x) has a turning point
Find 6x3+11x-18x-11 divided by 2x+1
3x2+4x-11
What are the transformations from the parent function resulting in f(x)=-(x+1)4?
Reflection across the x-axis
Translation left 1 unit
What is the behavior of the graph at each zero of f(x)=(x+3)3(x-6)4(x-1) ?
at x=-3, f(x) crosses the x-axis
at x=6, f(x) has a turning point
at x=1, f(x) crosses the x-axis
Remainder of 9
or 9/(x-2)