IM 9 Advanced
Polynomials Unit Review Exercises
I) NON- CALCULATOR: Complete the following for each of the polynomial FUNctions below.
1) 𝑓 𝑥 = 4𝑥 ! − 8𝑥 ! − 60𝑥 !
2) 𝑔 𝑥 = −𝑥 ! + 8𝑥 ! − 16𝑥 !
3) ℎ 𝑥 = 𝑥 𝑥 − 2
!
𝑥+3
!
a) Based on the degree, state how many zeros the function could possibly have.
b) Based on the degree, state how many turning points the function could possibly have.
c) Keeping the sign of the leading coefficient in mind, state the general shape the functions will have
and what its “end behavior” will be. (As 𝑥 → ∞, 𝑓 𝑥 → ______ . As 𝑥 → −∞, 𝑓 𝑥 → ______ .)
d) Find the location of the y-intercept.
e) Factor the function to find the location of the x-intercepts. State any repeated roots.
f) Using the points and shape found above, make an ACCURATE sketch of the function.
II) NON- CALCULATOR: Complete the following for each of the polynomial FUNctions below.
a)
b)
c)
d)
Whatisthedegreeofthepolynomial?
Whatisthesignoftheleadingcoefficient?
Arethereanyrepeatedrootsandifsohowdoyouknow?
Writetheequationofthepolynomialinfactoredform,beingsuretofindacorrectavalue.
Intercepts:(-3,0),(-2,0),(-1,0),(2,0),(3,0)and(0,-72) Intercepts:(-1,0),(1,0),(2,0)and(0,4)
Intercepts:(-2,0),(-1,0),(2,0)and(0,-8) Intercepts:(-3,0),(-2,0),(-1,0),(2,0)and(0,-60)
III) CALCULATOR: Complete the following for each of the polynomial FUNctions below.
a)
b)
c)
d)
Findthecoordinatesofthey-interceptofthefunction.
Findthecoordinatesofthex-interceptsofthefunction.
Findthecoordinatesofallturningpoints(maxormin)ofthefunction.
UsingALLoftheaboveinformationandyourcalculatorasaguide,sketchagraphofthe
function.Clearlyscaleyouraxesandlabelallaxesinterceptsandturningpoints.
𝑦 = −2.5𝑥 ! − 0.25𝑥 ! + .5𝑥 ! + 4.25𝑥 − 5.5
𝑦 = −2𝑥 ! − 5𝑥 ! + .05𝑥 ! − 5.5
𝑦 = −2𝑥 ! − 5𝑥 ! + 5𝑥 ! 𝑦 = −5𝑥 ! + .5𝑥 ! + 4𝑥 + 5.5