Question

URGENT HELP, PLEASE

Answer 1

Write a quadratic function in the standard form y 5 ax2 1 bx 1 c, such that a, b, and c do not equal zero.

a) Describe at least two methods that can be used to determine the graph of your function.

b) Write the quadratic equation in vertex form.

c) Find the maximum or minimum value. Explain how you can determine this value.

d) Determine the zeros of your function. Give an algebraic reason for the existence or nonexistence of real-values zeros of your quadratic function.

Answer 2

where exactly are you stuck?

Answer 3

"Write a quadratic function in the standard form y 5 ax2 1 bx 1 c, such that a, b, and c do not equal zero. " there...

Answer 4

y 5 ax2 1 bx 1 c
is that suppose to be:

\[y = ax^{2} + bx + c\]

Answer 5

or is that actually how it is written?

what I wrote is standard form for a quadratic equation

a, b and c are just variables, make them any number you want
I will set a = 1, b = 2 and c = 1

so we get,

1x^(2) + 2x + 1 = y
=
x^(2) + 2x + 1 = y

Answer 6

I assume this is for introduction to calculus?

Answer 7

that's where Im confused... the directions are exactly written as I wrote it :(

Answer 8

yeah that makes no sense best just to stick with what I wrote as that is standard form for a quardratic equation

Answer 9

if this is for an assignment I would recommend contacting your teacher or just accepting what I wrote

Answer 10

I thin 5 is the = sign, 1 is the + sign lol

Answer 11

think*

Answer 12

what would the "5" mean though.. ?

Answer 13

why write it like that though, and not being straight forward with the = and + sign? :(

Answer 14

I dont know maybe the person who wrote it was high, it doesn't matter, just trust me what I posted is the standard form just use that.

Answer 15

anyother questions?

Answer 16

okay so my equation is y = xˆ2 + 2x + 1 right?

Answer 17

yes I would use that you could just use all 1s as well it doesn't matter I just used that because it factors easily

Answer 18

I'm also having difficulty finding methods that can be used to determine the graph of my function... this is so hard :(

Answer 19

no it isn't trust me, well you can at least come up with 1

Answer 20

is the vertical line test one?

Answer 21

you dont know what the vertical line test is do you?

Answer 22

It's a test in order to find if a graph is a function or not, right? If two dots are in the vertical line anywhere on the graph, it's not a function.

Answer 23

yes :)

but how does that help you graph a function?

Answer 24

I'm having difficult understanding what "determine" the graph of your function means.. the keyword "determine"..

Answer 25

determine means to figure out, or discover

Answer 26

its asking how you would draw the graph of the function

Answer 27

Drawing a graph is like 30% of introduction to calculus

Answer 28

and like 5% of calculus 1

Answer 29

but it asks me to find 2 methods.. is one of them vertex form?

Answer 30

well the vortex form can be helpful (I never use it).

What is the first way you learned to draw a graph?

Answer 31

I'm actually confused about the methods of which i can choose..

Answer 32

well I draw the x and y axis, and plug in the coordinates given

Answer 33

exactly so thats your first answer

Answer 34

..what? so there is no specific method with a specific name? :s

Answer 35

am I thinking too hard?

Answer 36

well the first method, plug in numbers into the function and acquire points then draw a line to connect those points

Answer 37

but that is rough and takes longer than the other method

Answer 38

now considering you are in a calculus course what is the second thing we can use?

Answer 39

I'm still having difficulty understanding how I can list two methods that determine the graph of the function y = xˆ2 +2x + 1 :(

Answer 40

this is algebra 2 actually.. hard class this one i guess..

Answer 41

well pick a range of x values


so

-100, -50, -30, -10, -9, -7, -5, -2, 0, 2, 5, 7, 9, 10, 30, 50, 100

Answer 42

plug those into your equation to acquire points, then connect the points

Answer 43

I picked high numbers so we could see which direction the function is going towards infinity

Answer 44

have you touched on calculus at all? or is this stricktly using algebra?

Answer 45

okay so the first method is to pick a range of x values and plug them into my equation to acquire points, then I connect the points.

Answer 46

I'm not familiar with calculus.. all I know my course is titled Algebra 2

Answer 47

ok for the second method I guss you could graph transformations but to be honest I have no idea how to do those I think I have a note on it that might be useful for you if you want it

Answer 48

is transformations algebra 2? never heard it :s

Answer 49

you can use calculus to easily graph functions that was my second method but I guess graph transformations is the only other have they been addressed in your class.

Graph transformations is when you take a easy to draw function and use it to draw a more complicated function

Answer 50

ugh my grammar today it is terriable

Answer 51

don't worry its fine :))

Answer 52

well graph transformation was breifly addressed in my functions class way back when.

Answer 53

is there another method other than graph transformations? I don't'think we've covered that :s

Answer 54

yes, I guess you could write it in vertex form determine its vertex and then just determine its y and x intercepts and just use those to draw the function

Answer 55

by the way what about the equation f(x) = a(x-h)ˆ2 + k, where (h,k) are the vertex?

Answer 56

based on the fact you know it is a parabola

Answer 57

so there are your two methods

Answer 58

so you're saying this is vertex form?> f(x) = a(x-h)ˆ2 + k

Answer 59

do you know what a vertex is?

Answer 60

(0,0) of the graph?

Answer 61

well if the equation was x^2

Answer 62

wait no, a vertex is a point

Answer 63

it is a point in the graph where the functions changes I'm pretty sure, or the origin point of a parabola.

if you have the vertex of a parabola you can easily draw it

Answer 64

if you have its x and y intercepts

Answer 65

it is also the max or the min of a parabola

Answer 66

do you understand?

Answer 67

alright, I think I get it :)

Answer 68

so all i have left to do is findiding the maximum or minimum value, which i can do with calculator right?

Answer 69

oh yeah and also, have to determine the zero of the function, of which i can do with the calculator right?

Answer 70

well if you have a graphing calculator or an infinite amount of time if you plan on just punching in numbers

Answer 71

for this problem you can just factor it to figure out its vertex

Answer 72

to find the vertex I got y = (xˆ2 + 2x + 1) + 1 - 1(1)

Answer 73

if you picked a harder quadratic equation you would have to complete the square here is a good explanation of how to get an equation in vertex form:

http://answers.yahoo.com/question/index?qid=20080126030411AAqki2I

here is a good video on how to complete the square (seriously, patrickjmt is great I recommend his videos highly)

http://www.youtube.com/watch?v=xGOQYTo9AKY

Answer 74

well in your case the quadratic equation is already a square, you should be able to look at it and tell that it is just

(x+1)^(2)

think about it 1*1 = 1 and 1x + 1x = 2x

Answer 75

I've watched patrickmjt before! :)

Answer 76

wait so my vertex would be y = (x+1)ˆ2 + 1?

Answer 77

thus the vertex is -1,0

Answer 78

well I cant remember the completing the square method (although, it can be helpful if solving integrals later on but even then smeh) I guess I could relearn it to show you if you really want me to

Answer 79

actually, it already says it on the yahooanswers page you gave me! : )

Answer 80

Just a heads up be careful of yahoo answers that site is full of missinformation

Answer 81

i'll keep that in mind for sure

Answer 82

anything else you need help with or no?

Answer 83

last thing :)

Answer 84

i can determine the zero of the function, but how do i give an algebraic reason for it if i do it on calculator? (i have ti84)

Answer 85

I assume it means the y-intercept and x-intercepts?

Answer 86

do it on paper

x-intercept, set y = 0
so you will have no points, or points where
(y, 0)


y-intercept, set x = 0
so you will have 1 point or no point
(0,y)

Answer 87

crud I made a mistake

Answer 88

x-intercept,
set y = 0
so you will have no points, or points where
(x, 0)

Answer 89

amazing!

Answer 90

you have helped me with everything, thank you SO SO MUCH! :)

Answer 91

I guess by zeros of the function they are asking for x-interscepts,

its not a problem it kills time for me

Answer 92

but I would just include both I dont know it is your call

Answer 93

I think I'll go for the x intercept

Answer 94

thank you LOADS :D