Question

ALGEBRA 2, UNIT 3, LESSON 5:
Graphing Quadratics
ALTERNATE ASSIGNMENT

Did you know parabolas are all around you in the real world!? If you’ve traveled to the Midwest, you may have seen this one before:
The Gateway Arch in St. Louis, Missouri is a 630-foot high monument that was first designed in 1947. Construction of the stainless steel arch lasted many years, and the arch was not completed until October 1965. It was created as a monument to the westward expansion of the United States, and to this day it is the tallest man-made monument in America, as well as the world’s tallest arch

Answer 1

Use the following function to complete #1-3 below f(x)=2(x-6)^2+4

1) Using complete sentences, explain how to convert f(x) into standard form.
Give the final standard form equation in your answer.

2) Graph f(x) by hand or with technology. Include a photo or screenshot of the parabola.

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

Answer 2

hey XD

Answer 3

hi lol im still stuff on this problem for a week :(

Answer 4

@RANE
@mathgeek27
@mathmath333
@rwestfall_ca
@MakaylaTracy
@walters

Answer 5

Its ok were here to help YOU

Answer 6

i might be able to help but then again im only a freshman :(

Answer 7

thanks i really need it pple gave me the answers but never told me how they got it n what i need is lik to say how i got the answer in complete sentences and so im so lost

Answer 8

i understand @J-bird

Answer 9

\[ f(x)=2(x-6)^2+4 \]
1) Using complete sentences, explain how to convert f(x) into standard form.

Multiply out, combine like terms

Answer 10

i could do the problem and graph it and all but i dont think i could explain :P

Answer 11

kind of a short sentence, but that is all there is to it
\[f(x)=2(x-6)^2+4=2(x-6)(x-6)+4=...\]

Answer 12

the standard form of the porabola is y=2x^2-27x+76 which is #1

Answer 13

right ?

Answer 14

Good Job @satellite73

Answer 15

2) Graph f(x) by hand or with technology. Include a photo or screenshot of the parabola.

well then lets use technology !
http://www.wolframalpha.com/input/?i=2%28x-6%29^2%2B4

Answer 16

ok :)

Answer 17

btw technology also multiplied out for you, you see it is \[f(x)=2 x^2-24 x+76\]

Answer 18

wait but which one would it be ?

Answer 19

which is not what you had

Answer 20

ooo :( wow thank you if u didnt catch thst i would hsve lost major points and i cant aaford that

Answer 21

the pictures are both the same, only the scale is different
i would go with the top one though

Answer 22

ok :)

Answer 23

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

average rate of change is f of seven minus f of four divided by seven minus four
jeez the sentence is kind of silly, it is
\[\frac{f(7)-f(4)}{7-4}\]

Answer 24

tell FLVS this "complete sentence" nonsense is written by morons
you can compute those numbers i am sure
good luck

Answer 25

? so 3 divided by 3 lol

Answer 26

i will lol half the work they give me make no sense or have a million typos

Answer 27

i didn't check it
\(7-4=3\) for sure
you want me to check the numerator also?

Answer 28

hey i'm FLVS :( ;*(

Answer 29

yes please

Answer 30

ok it is wrong

Answer 31

? what do u mean

Answer 32

@cuteandsexy thats great please post your question in your post and no here thats spam ^_^ thank you for complying

Answer 33

\[f(7)=2(7-6)^2+4=2\times 1+4=6\]

Answer 34

\[f(4)=2(4-6)^2+4=2\times 4+4=12\]

Answer 35

\[f(6)-f(4)=6-12=-6\]

Answer 36

and
\[\frac{f(7)-f(4)}{7-4}=\frac{-6}{3}=-2\]

Answer 37

0_0 ? wait how would it equal -6 it makes no sense i thought it was 3/3?

Answer 38

i don't know another way to say it
compute
\[f(7)\]
i get \[f(7)=6\]
compute \[f(4)\]
i get \[f(4)=12\]

Answer 39

then compute
\[\frac{f(7)-f(4)}{7-4}=\frac{6-12}{3}=\frac{-6}{3}=-2\]

Answer 40

are u using wolf of alpha if so it gives wrong answers sometimes try mathway ...i dont show u the work but it does the answer

Answer 41

i did it by hand

Answer 42

nope never mind that is right wow math has many secrets

Answer 43

do you know how to compute \(f(7)\) ?

Answer 44

no i put it in the math site and yup u were right im so sorry i wasnt telling u u were wrong i jus thought it was odd bc it didnt make sense at first lol

Answer 45

@phi is all this right ?

Answer 46

You could make it your goal to learn how to figure out f(7)
\[ f(x)=2(x-6)^2+4 \]
f(x) is a "short name" for the formula
the (x) part is to remind us the formula uses "x"

f(7) is short for:
find the "x" in the formula. Erase it, and put in its place the number 7
can you do that ?

Answer 47

I JUST WANNA MAKE DOULE SURE BEFORE I WRITE IT ALL OUT AND TRUN IT IN im lik almost a whole week overdue

Answer 48

yes i think yes

Answer 49

yes i can sorry yes i can replace all x's with the number 7 :)

Answer 50

write down the formula with x replaced with 7

Answer 51

you should get
f(x)=2(x-6)^2+4
f(7) = 2(7-6)^2 + 4

Answer 52

Do you remember your "order of operations" ?
to simplify
2(7-6)^2 + 4
what do we do first ?

Answer 53

pemdas?

Answer 54

paranthesis

Answer 55

yes, and what do you get ? i.e. 7-6

Answer 56

so 2(1)^2+4 then we do exponents

Answer 57

yes

Answer 58

so then we get 2(1)+4 then we multiply

Answer 59

so we get 2+4 and then we dont have any division to do so we go to addition and get 6 as our answer right ?

Answer 60

what do we do next ?

Answer 61

exactly
f(7) = 6
that means when x is 7, f(7) is 6
or (7,6) is a point on the curve.

Answer 62

average rate of change for f(x) from x = 4 to x = 7.

the "rate of change" is change in f(x) divided by change in x
in other words we have to figure out
f(7) - f(4) (that is how much f(x) changes between x=4 and x=7)

so we need to find f(4)
any idea how ?

Answer 63

O_O wow i didnt know that omg thank you can u help me with more like is my problem rightt ? the one that i did with sattelitte ? and now i know omg thanks my teacher in flvs doesnt teach sqwat

Answer 64

yes hang on n ill right it out

Answer 65

2(4-6)^2+4 right ?

Answer 66

yes

Answer 67

so then i do paranthisis -2 so i get 2(-2)^2+4

Answer 68

yes

Answer 69

then exponents 4 so 2(4)+4 then i multiply and i get 8+4 and since there is no division i do addition so i get 12 as my answer right ?

Answer 70

yes, so when x is 4, f(x) is 12
(4,12) is also a point on the curve.
the vertex (which we can get from the equation) is (6,4)

if we plot those 3 points, it looks like this

Answer 71

now we can find the difference between f(7) and f(4)
f(7) - f(4) is ?

Answer 72

wait im sorry so interupt but why is there 3 points?

Answer 73

Oh, I know (and probably they want you to know) that when you have an equation that looks like this:
a (x - h)^2 + k
that the vertex (the top or bottom of the parabola) is at (h,k)
if we match that formula with
2(x-6)^2+4

we see the h matches with 6
and k with 4
the vertex is at (h,k) , which is (6,4)

I did that to help you plot this curve.

Answer 74

meanwhile, we now want to find
f(7) - f(4)
find the numbers for f(7) and f(4) which you figured out. and do the subtraction
can you do that ?

Answer 75

yes well i know f(7) is 6

Answer 76

yes

Answer 77

f(4) is 12

Answer 78

yes

Answer 79

so then i do 6-12

Answer 80

yes

Answer 81

and i get -6

Answer 82

that says from point A to point C (in the graph I posted), we moved down 6 steps
(from 12 down 6 steps to get to 6)

the average rate of change for f(x) from x = 4 to x = 7.
is the change in f(x) divided by the change in x

the change in x is 7-4 = 3

now we do change in f(x) divided by change in x
i.e. (f(7)-f(4) ) / (7-4)

Answer 83

btw, if we drew a line from point A to point C, we are finding the slope of that line
slope is (change in y)/(change in x)

and we usually match f(x) with y when we plot

Answer 84

6-12/6-12 right ?

Answer 85

or is it 6-12/ (7-4)?

Answer 86

the second. change in f(x) divided by change in x

or, if you know how to find the slope between 2 points, it is the slope between
(4,12) and (7,6)

Answer 87

wait so 4-12 divided by 7-6 so 4-12/7-6

Answer 88

and it would be good to write it as
(6-12)/ (7-4)

because if we followed order of operations
6 - 12/(7-4) would do the wrong thing.

Answer 89

so -8/1

Answer 90

ooooooo bc its y1-y2/x1-x2 right ?

Answer 91

I think I confused you with the slope idea.

it is the difference in the y values (the 2nd number)
divided by the difference in the x values.

Answer 92

*** 4-12 divided by 7-6
that is x-y divided by x-y which is not what we want

Answer 93

oooo ok sorry my bad lol i had my formulas for slope wrong my bad

Answer 94

si its x1-y1/ y2-x2 right ?

Answer 95

*** y1-y2/x1-x2 right ?
this is correct. But I would use parens
(y1-y2)/(x1-x2)

Answer 96

just be careful and think out each step. pick out y1
pick out y2
write it down
then do the same for the x's