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College Algebra > Test 3 > Flashcards

Test 3 Flashcards

1
Q

How to tell if something is a function

A
  • exponents are positive integers

- no imaginary numbers

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2
Q

Quadratic function (ax2+bx+c) vertex

A

(-b/2a, plug in and solve for y)

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3
Q

Quadratic function (ax2+bx+c) axis of symmetry

A

x= -b/2a

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4
Q

Quadratic function (ax2+bx+c) y-intercept

A

let x=0 and solve for y

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5
Q

Quadratic function (ax2+bx+c) x-intercepts

A
  • if b2-4ac>0, then factor/use quadratic equation
  • if b2-4ac=0, the intercept is -b/2a
  • if b2-4ac
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6
Q

Quadratic function (ax2+bx+c) direction of opening

A

up if a>0, and down if a

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7
Q

vertex form

A

f(x)=a(x-h)^2+k

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8
Q

f(x)=a(x-h)^2+k vertex

A

(h,k)

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9
Q

f(x)=a(x-h)^2+k axis of symmetry

A

x=h

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10
Q

f(x)=a(x-h)^2+k y-int

A

let x=0, solve for y

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11
Q

f(x)=a(x-h)^2+k x-int

A

let y=0, solve for x

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12
Q

f(x)=a(x-h)^2+k direction of opening

A

up if a>0 and down if a

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13
Q

height velocity formula

A

s(t)= -16t^2 + Vot + So

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14
Q

S(t)

A

height at a given time

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15
Q

t

A

time

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16
Q

Vot

A

initial velocity

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17
Q

So

A

initial height

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18
Q

maximum height

A

vertex

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19
Q

what interval of time, greater than blank feet

A

set it equal to blank, make into a quadratic and use the quadratic formula

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20
Q

Find two numbers whose sum is __ and whose product is the maximum possible value

A
  • make two equations
  • make into quadratic
  • use -b/2a to find x
  • plug in x to find y
21
Q

Express in the form f(x)=(x-k)q(x)+r

A
  • (x-k)= what you divide by
  • q(x)=answer in squared form
  • r=remainder
22
Q

remainder theorem

A

if you plug f(x) into the equation, you will get the remainder the same as if you did synthetic division
- answer is the remainder

23
Q

factor theorem

A

(x-k) is only a factor if f(k)=0

24
Q

how to factor equation using linear factors given a zero

A
  • use the zero in synthetic division to get quadratic
  • factor the equation to get the other zeros
  • highest power=number of zeros
  • Factor the three zeros (opposites)
25
Q

possible rational roots

A

P/Q- last number/first coefficient

26
Q

actual rational roots

A

plug into calculator and prove with synthetic division

27
Q

factor rational roots

A
  • highest exponent-number of roots/factors

- factor the zeros out individually

28
Q

Find all the zeros and their multiplicities given factored equation

A
  • factor completely out
  • exponent=multiplicity
  • x^2 inside ( )= +- square root, multiplicity 1
29
Q

a in y=a(x-h)^n+k translations

A
  • if lal>1, the graph is stretched vertically (skinner)

- if 0

30
Q

multiplicity 1 looks like

A

line

31
Q

multiplicity of even number looks like

A

parabola

32
Q

multiplicity of odd number looks like

A

squiggle

33
Q

Positive and even

A

up and up

34
Q

Negative and even

A

down and down

35
Q

positive and odd

A

down and up

36
Q

negative and odd

A

up and down

37
Q

graphing polynomial function (more than x2)

A
  1. Find all zeros and plot them (calculator)
  2. Find y-int
  3. determine more points to show shape
  4. use end behavior
38
Q

factored out polynomial function graphing

A
  • number of zeros=sum of exponents
  • exponents show multiplicity
  • same as usual
39
Q

use synthetic division to show has a zero between _ and _

A

do both and its one remainder is negative, and one is positive, then it does

40
Q

Rational functions

A

f(x)=p(x)/q(x)

41
Q

vertical asymptotes for rational functions

A

set denominator=0 and solve for x

- x=

42
Q

horizontal asymptotes for rational functions

A
  • degree N D none unless exactly greater than one
43
Q

If N > D by exactly one

A
  • oblique/slant asymptote
  • use synthetic division and divide by vertical asymptote value
  • first two numbers use in line equation
44
Q

y-int for rational functions

A

let x=0 and solve for y

45
Q

x-int for rational functions

A

set numerator=0 and solve for x

46
Q

how to identify holes

A

factor out numerator, if anything cancels, set to 0, hole at x=opposite

47
Q

max area of a fence

A
  • L X W for equation
  • -b/2a
  • plug back into equation
48
Q

what rainfall produces the maximum number of mosquitoes

A

-b/2a is your answer

College Algebra (5 decks)

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