Test 3 Flashcards
How to tell if something is a function
- exponents are positive integers
- no imaginary numbers
Quadratic function (ax2+bx+c) vertex
(-b/2a, plug in and solve for y)
Quadratic function (ax2+bx+c) axis of symmetry
x= -b/2a
Quadratic function (ax2+bx+c) y-intercept
let x=0 and solve for y
Quadratic function (ax2+bx+c) x-intercepts
- if b2-4ac>0, then factor/use quadratic equation
- if b2-4ac=0, the intercept is -b/2a
- if b2-4ac
Quadratic function (ax2+bx+c) direction of opening
up if a>0, and down if a
vertex form
f(x)=a(x-h)^2+k
f(x)=a(x-h)^2+k vertex
(h,k)
f(x)=a(x-h)^2+k axis of symmetry
x=h
f(x)=a(x-h)^2+k y-int
let x=0, solve for y
f(x)=a(x-h)^2+k x-int
let y=0, solve for x
f(x)=a(x-h)^2+k direction of opening
up if a>0 and down if a
height velocity formula
s(t)= -16t^2 + Vot + So
S(t)
height at a given time
t
time
Vot
initial velocity
So
initial height
maximum height
vertex
what interval of time, greater than blank feet
set it equal to blank, make into a quadratic and use the quadratic formula
Find two numbers whose sum is __ and whose product is the maximum possible value
- make two equations
- make into quadratic
- use -b/2a to find x
- plug in x to find y
Express in the form f(x)=(x-k)q(x)+r
- (x-k)= what you divide by
- q(x)=answer in squared form
- r=remainder
remainder theorem
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
factor theorem
(x-k) is only a factor if f(k)=0
how to factor equation using linear factors given a zero
- 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)
possible rational roots
P/Q- last number/first coefficient
actual rational roots
plug into calculator and prove with synthetic division
factor rational roots
- highest exponent-number of roots/factors
- factor the zeros out individually
Find all the zeros and their multiplicities given factored equation
- factor completely out
- exponent=multiplicity
- x^2 inside ( )= +- square root, multiplicity 1
a in y=a(x-h)^n+k translations
- if lal>1, the graph is stretched vertically (skinner)
- if 0
multiplicity 1 looks like
line
multiplicity of even number looks like
parabola
multiplicity of odd number looks like
squiggle
Positive and even
up and up
Negative and even
down and down
positive and odd
down and up
negative and odd
up and down
graphing polynomial function (more than x2)
- Find all zeros and plot them (calculator)
- Find y-int
- determine more points to show shape
- use end behavior
factored out polynomial function graphing
- number of zeros=sum of exponents
- exponents show multiplicity
- same as usual
use synthetic division to show has a zero between _ and _
do both and its one remainder is negative, and one is positive, then it does
Rational functions
f(x)=p(x)/q(x)
vertical asymptotes for rational functions
set denominator=0 and solve for x
- x=
horizontal asymptotes for rational functions
- degree N D none unless exactly greater than one
If N > D by exactly one
- oblique/slant asymptote
- use synthetic division and divide by vertical asymptote value
- first two numbers use in line equation
y-int for rational functions
let x=0 and solve for y
x-int for rational functions
set numerator=0 and solve for x
how to identify holes
factor out numerator, if anything cancels, set to 0, hole at x=opposite
max area of a fence
- L X W for equation
- -b/2a
- plug back into equation
what rainfall produces the maximum number of mosquitoes
-b/2a is your answer
