Question

Quadratic Functions [Halp the Smores]

Answer 1

Create a quadratic function, f(x), in vertex form. The a should be between 4 and –4, the h will be 8, and the k will be 20. Write your equation below.

Using complete sentences, explain how to convert your birthday function into standard form.

Create two additional quadratic functions, g(x) and h(x).
The function g(x) will open the same direction as f(x), have the same vertex, but will be narrower.
The function h(x) will open in the opposite direction as f(x), have the same vertex, but will be wider than f(x).
Write your functions below and explain in complete sentences why those functions will meet the requirements in the question.

Graph your functions. Include your graph below.

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

Explain the appropriate translations of your graphs, if you were born two months earlier and 5 days later. Use complete sentences.

Answer 2

Graph to use, the least I could do. :B
http://i.imgur.com/HbYg7Nm.jpg

Answer 3

Now, the quadratic equation looks like this:
\[\Large f(x) = a(x-h)^2 + k\]

Answer 4

Wait a sec, what the heck is a birthday function???

Answer 5

@terenzreignz It's pretty much what the original equation is. That's what I'm assuming anyways

Answer 6

Don't assume... did you know of this birthday function?

Answer 7

Not really actually. I can call my teacher quick to see what she says?

Answer 8

Please do ^_^

Answer 9

Okay~ Be back in 5

Answer 10

@terenzreignz Yeah, she said it was the original equation from the start.

Answer 11

oh okay.
So...
\[\Large f(x) = a(x-h)^2 + k\]
You ARE given the values of h and k, right?

Answer 12

Correct, h = 8 and k = 20.

Answer 13

Okay, so I suggest we already substitute.
\[\Large f(x) = a(x-8)^2 + 20\]

Answer 14

Now, what's your value for a?

Answer 15

I don't see any information for a, so we must have to find it?

Answer 16

No. I'm quite literal when I say YOUR value for a.
I believe you're allowed to choose one for yourself, provided, it falls within the acceptable range prescribed in your question...

Answer 17

So, I guess let's choose 10? I'm not sure how that works; slightly confused.

Answer 18

Well you can't choose that :P
You can only choose something between 4 and -4.
Did you even read your question? XD

Answer 19

I must of read over that part... LOL okay let's use 3

Answer 20

Fine.
\[\Large f(x) = 3(x-8)^2 + 20\]

Answer 21

Now, can you express this in standard form/

Answer 22

Okay. So I tried looking through my notes for expressing them in standard and I don't have anything. Remind me what the steps would be?

Answer 23

Well, first, expand the (x-8)^2

Answer 24

That would be...
x^2 - 16x + 64 ?

Answer 25

That's good.
\[\Large f(x) = 3(x^2 - 16x + 64) + 20\]
Now distribute the 3...

Answer 26

That would be multiplying 3 to everything in that parenthesis (x2...), correct?

Answer 27

Of course...

Answer 28

3x2 - (3)16x + 192 ?

Answer 29

surely you can do something about 3*16?
And the +20 at the end, that does not simply disappear.

Answer 30

I though since it was already paired with x, I would put it in parenthesis next to it (homeschool ruined me, LOL)

So it would be (3x2 - 48x + 192) + 60

Answer 31

LOL +20 was NEVER inside the parentheses.
... try again :P

Answer 32

Oops, I forgot that you don't touch it.

(3x2 - 48x + 192) + 20

Answer 33

Okay, now you can do away with the parentheses, and "unite" the 192 and the +20 since they are like terms.

Answer 34

3x2 - 48x + 212

Answer 35

Lo and behold, it's already in standard form :)

Answer 36

Yay, I am Einstein. lol :B

Answer 37

Time for the next bit then?

Answer 38

Create g and h

Answer 39

One second, I have to be right back.

Answer 40

Alright back, and how will we make g & h?

Answer 41

Start with g.
It has to have the same vertex, so h and k remain 8 and 20 respectively, aye

Answer 42

?

Answer 43

I can agree on that.

Answer 44

Okay, it should point upwards as well... how do you make sure of that?

Answer 45

Keep it as a positive number?

Answer 46

By the way
\[\Large f(x) = \color{blue}a(x-\color{red}h)^2 + \color{green}k\]
h and k determine the vertex, this you already know :)
a determines where it points (positive a means it open up, negative a means it opens down)

also, check |a|
The bigger |a| gets, the narrower the opening.

Now, g has to open in the same direction as f, so what should be the sign on the a in g?

Answer 47

I'm not sure actually, I suck at graphs. I would go ahead and say negative so it points up when it opens down.

Answer 48

No, of course not, it should open in the same direction as f, and f has a positive value for a, so a should also be positive for g. Capisce?

Answer 49

Kapeesh ('Murica)

Answer 50

Okay, also, it says g should be narrower... so the value of the a for g has to be bigger than the one for f. Comprendes?

Answer 51

Okay...

Answer 52

So, pick a value for a (for g)
anything, as long as it's bigger than 3.

Answer 53

4 :B

Answer 54

Fine.
\[\Large g(x) = 4(x-8)^2 + 20\]

Answer 55

Okay

Answer 56

What about h?

Answer 57

Wouldn't we keep that the same?

Answer 58

We would keep h and k the same, true, but this time it has to open in an OPPOSITE direction to f.
So a has to be...(positive/negative)?

Answer 59

Negative

Answer 60

mhmm. and it also has to be wider than f. so its absolute value must be less than 3.
pick such a number.

Answer 61

-1? o -o

Answer 62

sure, why not? :)
\[\Large h(x) = -(x-8)^2 + 20\]
and there you have it :)

Answer 63

How would that be graphed?

Answer 64

uh-oh... I'm not really the best to teach how to graph... but, I'll try.
Start with f.

Answer 65

\[\Large f(x) = 3(x-8)^2 + 20\]

Answer 66

Well you could graph it and explain how you did? x.x

Answer 67

Nah, that wouldn't do. :P
It's all about identifying a few points and then just tracing the pattern.
Observe... obviously, when x = 8, f(x) = 20, right?

Answer 68

Correct and it would! ;-;

Answer 69

It wouldn't. That would be spoonfeeding, and I know you don't want to be treated like a baby, right? ;)

Anyway, pick another value for x, besides 8, how about 9?

Answer 70

Pffft, with graphs.. spoonfeeding sounds good.
As for 9, sure.

Answer 71

if x = 9, what is f(x)?

Answer 72

f(9)? x.x

Answer 73

yes... so... f(9) is equal to...?

Answer 74

Oh wait, you meant with f(x)=3(x−8)2+20 ?

Answer 75

duh LOL

Answer 76

FORGET YOU! >;U

So first I'd replace all the x's..
f(9) = 3(9 - 8)2 + 20.

f(9)= 3(1)^2 + 20

f(9) = 23

Answer 77

Forget me?
Who am I? D:

Answer 78

;-; Stop it.

Answer 79

Okay, you now have two points, (8,20) and (9,23)
what about x = 7

Answer 80

f(x)=3(x−8)2+20

f(7) = 3(7-8)^2 + 20

-3 + 20 = 17

Answer 81

okay, that's another point (7,17)
Try x = 10 and x = 6 too.

Answer 82

f(10) = 3(10-8)^2 + 20

f(10)= 32

f(6) = 3(6-8)^2 + 20
f(6) = 8

Answer 83

@terenzreignz I have to go in like 15 minutes.. we must hurry!

Answer 84

Okay, that's five points already :D
(6,8), (7,17), (8,20) [vertex], (9,23), (10,32)

Just plot these points, they should give you an idea on what the graph is gonna look like.

Answer 85

Don't tag me when I'm already here, LOL
and it's TJ ;)

Answer 86

Have you plotted them yet?

Answer 87

Not yet, I'll do it now.

Answer 88

You're the one in a hurry :P
It should look like a U-shape of sorts.

Answer 89

The graph I have isn't big enough. Anyways, I have to go for now.

Answer 90

aww.. okay :)

Answer 91

birthday function?

Answer 92

@satellite73 Yeah, I verified that with my teacher already and it's the function provided.

Answer 93

For whoever decided to help, just help me off of what terenz already provided so I can finish this. It's extremely important ;_;

Answer 94

@kelliegirl33

Answer 95

@ehuman @nonamenever @angel12310

Answer 96

I really need to get this done, I'd like if someone helped. :T

Answer 97

http://openstudy.com/study#/updates/52570bd1e4b0ede9e447371c