Solving(Quadratic(and(Other(Equations( 3.3(!
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Ready,'Set,'Go!'''
Ready'Topic:!Meaning!of!Exponents!!In'the'table'below'there'is'a'column'for'the'exponential'form,'the'meaning'of'that'form,'which'is'a'list'of'factors'and'the'standard'form'of'the'number.'Fill'in'the'form'that'is'missing.'
Exponential!form! List!of!factors! Standard!Form!
5!! 5 ∙ 5 ∙ 5! 125!
1a.! 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7! b.!
2.! 2!"! a.! b.!
3a.! b.! 81!
4.! 11!! a.! b.!
5a.! 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3! b.!
6a.! b.! 625!!'Provide'at'least'three'other'equivalent'forms'of'the'exponential'expression.'Use'rules'of'exponents'such'as'!! ∙ !!'='!!!'and' !! !'='!!'as'well'as'division'properties'and'others.'! 1st!Equivalent!Form! 2nd!Equivalent!Form! 3rd!Equivalent!Form!
7.!!!!2!"!=! ! ! !
8.!!!!!3!!=! ! ! !
9.!!!!!13!!!=! ! ! !
10.!!!!!7!!!=! ! ! !
11.!!!!!5!!=! ! ! !
!!!
Name:!
2013!www.flickr.com/photos/zooboing!!
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Solving(Quadratic(and(Other(Equations( 3.3(!
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Set'Topic:!Finding!equivalent!expressions!and!functions.!!Determine'whether'all'three'expressions'in'each'problem'below'are'equivalent.'Justify'why'or'why'they'are'not'equivalent.''12.!!!!!!!!!!!!5(3!!!)!!
15(3!!!)! !!(3
!)!!
!13.!!!!!!!!!!!!64!(2!!)! 64
2! !64 !
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14.!!!!!!!!!!!3(x41)+4! 3x!4!1! 3(x42)!+7!!
!15.!!!!!!!50 2!!! !!!
25 2!!!! ! 50 4! !!
16.!!!!!!!!30 1.05! ! 30 1.05!!!!! 30 1.05
!!!!
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17.!!!!!!!!20! 1.1! !!!
20! 1.1!! !!! !20 1.1
!!!!!
!Go'Topic:!Using!rules!of!exponents!!Simplify'each'expression.'Your'answer'should'still'be'in'exponential'form.'!18.!!!!!!!!7! ∙ 7! ∙ 7!! 19.!!!!! 3! !! 20.!!!!!! 5! ! ∙ 5!!
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21.!!!!!!!! ∙ !!! 22.!!!!!!!!!! ! 23.!!!!!!!! ∙ !! !!
24.!!!!!! !! ! ! 25.!!!!!!!!
!!! 26.!!!!!! !! !
!! !
27.!!!!! !! !
!! ! 28.!!!!!!!!!!!! ! 29.!!!!!!!
!!!"!!!!!! !
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Solving(Quadratic(and(Other(Equations( 3.4(!
!©"2013"MATHEMATICS"VISION"PROJECT"|"MVP"In"partnership"with"the"Utah"State"Office"of"Education"""
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Ready,'Set,'Go!''
Ready'Topic:!Standard!form!or!Quadratic!form!!In'each'of'the'quadratic'equations,'ax2!+!bx!+!c!=!0'identify'the'values'of'a,'b'and'c'.'!1.!!!x2!+!3x!+2!=!0! 2.!!!2x2!+!3x!+!1!=!0! 3.!!!x2!–!4x!–!12!=!0!!!!!!!a!=!!!!!!!!b!=!!!!!!!!c!=!!
!!!!!!a!=!!!!!!!!b!=!!!!!!!!c!=!!!!!!!!!
!!!!!!a!=!!!!!!!!b!=!!!!!!!!c!=!
! ! !Write'each'of'the'quadratic'expressions'in'factored'form.'4.!!!!!!x2!+!3x!+2! 5.!!!!!!2x2!+!3x!+!1! 6.!!!!!!x2!–!4x!–!12!
7.!!!!!!!x2!4!3x!+2! 8.!!!!!!!x2!–!5x!–!6! 9.!!!!!!!x2!–!4x!+!4!
10.!!!!x2!+!8x!–!20! 11.!!!!!x2!+!x!–!12! 12.!!!!!x2!–!7x!+!12!
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Name:!
2013!www.flickr.com/photos/zjootsuite!!
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Solving(Quadratic(and(Other(Equations( 3.4(!
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©"2013"MATHEMATICS"VISION"PROJECT"|"MVP"In"partnership"with"the"Utah"State"Office"of"Education"""
Licensed!under!the!Creative!Commons!Attribution4NonCommercial4ShareAlike!3.0!Unported!license"
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Set'Topic:!Radical!notation!and!rational!exponents!!Each'of'the'expressions'below'can'be'written'using'either'radical'notation,'' !!! ''or'rational'exponents''!
!! .''Rewrite'each'of'the'given'expressions'in'the'form'that'is'
missing.'Express'in'most'simplified'form.''! Radical!Form! Exponential!Form!
13.! 5!! ! !
14.! !! 16
!!!
15.! 5! ∙ 3!! ! !
16.! ! 9!! ∙ 9
!!!
17.! !!"!!"! ! !
18.! 27!!!!! !!!
19.! 32!!"243!!"
!! !
20.! ! 9!!!!!!
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!!Solve'the'equations'below,'use'radicals'or'rational'exponents'as'needed.'21.!!!!!! ! + 5 ! = 81! 22.!!!!!!!2 ! − 7 ! + 3 = 67!!!!!
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Solving(Quadratic(and(Other(Equations( 3.4(!
!©"2013"MATHEMATICS"VISION"PROJECT"|"MVP"In"partnership"with"the"Utah"State"Office"of"Education"""
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Go'Topic:!x4intercepts!and!y4intercepts!for!linear,!exponential!and!quadratic!!Given'the'function,'find'the'xBintercept'(s)'and'yBintercept'if'they'exist'and'then'use'them'to'graph'a'sketch'of'the'function.''23.!!!!!! ! = (! + 5)(! − 4)! 24.!!!!!! ! = 5(2!!!)!!
a.!!x4intercept(s):!!!!
b.!!y4intercept:! a.!!x4intercept(s):!!
b.!!y4intercept:!
25.!!!!!ℎ ! = −2(! + 3)!!
26.!!!!!! ! = !! − 4!
a.!!x4intercept(s):!!
b.!!y4intercept:! a.!!x4intercept(s):!!
b.!!y4intercept:!
'!
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1) Find the exact, simplified value of each expression without a calculator. If you are stuck, try
converting between radical and rational exponential notation first, and then simplify.
Sometimes, simplifying the exponent (or changing a decimal to a fraction) is very helpful.
a. 31
125 b. 2/164 c. 6/164
d. 2/181 e. 5/132 f. 4/181
g. 2/34 h. (64)2/3 i. 8 5/3
j. 93/2 k.9
4
3/2
l. 161.5
m. 273 2
n. 12523
o. 43 6
p. 5 2
q. 24 4
r. 35 5
2) A parabola has the function f(x) = 2(x + 3)2 – 5. It is translated to a new location, given by the
function g(x) = 2(x – 3)2 – 2. Describe the translation.
a. 6 left and 3 up b. 6 left and 3 down
c. 6 right and 3 down d. 6 right and 3 up
3) What is the highest point on the function y = -(x – 5)2 + 3?
a. 1,13 b. 0,22 c. 5,3 d. 5,3
