Test 3

Question 1

How to tell if something is a function

Answer 1

• exponents are positive integers

- no imaginary numbers

Question 2

Quadratic function (ax2+bx+c) vertex

Answer 2

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

Question 3

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

Answer 3

x= -b/2a

Question 4

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

Answer 4

let x=0 and solve for y

Question 5

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

Answer 5

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

Question 6

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

Answer 6

up if a>0, and down if a

Question 7

vertex form

Answer 7

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

Question 8

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

Answer 8

(h,k)

Question 9

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

Answer 9

x=h

Question 10

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

Answer 10

let x=0, solve for y

Question 11

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

Answer 11

let y=0, solve for x

Question 12

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

Answer 12

up if a>0 and down if a

Question 13

height velocity formula

Answer 13

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

Question 14

S(t)

Answer 14

height at a given time

Question 15

t

Answer 15

time

Question 16

Vot

Answer 16

initial velocity

Question 17

So

Answer 17

initial height

Question 18

maximum height

Answer 18

vertex

Question 19

what interval of time, greater than blank feet

Answer 19

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

Question 20

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

Answer 20

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

Question 21

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

Answer 21

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

Question 22

remainder theorem

Answer 22

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

Question 23

factor theorem

Answer 23

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

Question 24

how to factor equation using linear factors given a zero

Answer 24

• 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)

Question 25

possible rational roots

Answer 25

P/Q- last number/first coefficient

Question 26

actual rational roots

Answer 26

plug into calculator and prove with synthetic division

Question 27

factor rational roots

Answer 27

- highest exponent-number of roots/factors | - factor the zeros out individually

Question 28

Find all the zeros and their multiplicities given factored equation

Answer 28

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

Question 29

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

Answer 29

- if lal>1, the graph is stretched vertically (skinner) | - if 0

Question 30

multiplicity 1 looks like

Answer 30

line

Question 31

multiplicity of even number looks like

Answer 31

parabola

Question 32

multiplicity of odd number looks like

Answer 32

squiggle

Question 33

Positive and even

Answer 33

up and up

Question 34

Negative and even

Answer 34

down and down

Question 35

positive and odd

Answer 35

down and up

Question 36

negative and odd

Answer 36

up and down

Question 37

graphing polynomial function (more than x2)

Answer 37

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

Question 38

factored out polynomial function graphing

Answer 38

- number of zeros=sum of exponents - exponents show multiplicity - same as usual

Question 39

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

Answer 39

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

Question 40

Rational functions

Answer 40

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

Question 41

vertical asymptotes for rational functions

Answer 41

set denominator=0 and solve for x | - x=

Question 42

horizontal asymptotes for rational functions

Answer 42

- degree N D none unless exactly greater than one

Question 43

If N > D by exactly one

Answer 43

- oblique/slant asymptote - use synthetic division and divide by vertical asymptote value - first two numbers use in line equation

Question 44

y-int for rational functions

Answer 44

let x=0 and solve for y

Question 45

x-int for rational functions

Answer 45

set numerator=0 and solve for x

Question 46

how to identify holes

Answer 46

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

Question 47

max area of a fence

Answer 47

- L X W for equation - -b/2a - plug back into equation

Question 48

what rainfall produces the maximum number of mosquitoes

Answer 48

-b/2a is your answer