Question

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.

The equation for this parabola is y = -x2 + 36.

Answer 1

In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.

Analyze the two functions. Answer the following reflection questions in complete sentences.

What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?
What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.

Is the linear function you created with your table positive or negative? Explain.
What are the solutions or solution to the system of equations created? Explain what it or they represent.
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Answer 2

@dude e,e can i getz some help preaze

Answer 3

lol look at my question

Answer 4

In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.

-6 6
0 0

Answer 5

(-6,0) (6,0)

Answer 6

Yeah 2 posts have already been made for this question idk where you guys would like me to answer

Answer 7

This include much more information though


Anyway you dont need the zeroes of the rainbow for the table

Answer 8

if you dont have to add the 0 then i have to find 2 more numbers e.e hmmmm

Answer 9

so you chose the points -6,0 to 6,0

Answer 10

yes cause it says it makes a slanted line that cuts through the rainbow at two points and if you look at the graph

Answer 11

it has 2 points -6,0 and 6,0

Answer 12

Well yes but it’s an airplane, if we use those points the plane would be on the ground the whole time

Answer 13

can I use -6,0 to 0,36

Answer 14

would (-6,0) and (11,4) work?

Answer 15

-6,0 to 0,36 is okay

11, 4 is not on the graph but it works anyway

Answer 16

Anyway to create the equation of the line, use the slope between two points formula

\(\large \frac{\Delta y}{\Delta x}\) or \(\large \frac{y_2-y_1}{x_2-x_1}\)

Answer 17

Or rise/run

Answer 18

i thought of it in the way planes dont go straight up when they lift off they go diagonal then up so 11,4 would make it look like the airplane is rising

Answer 19

Yeah it works, I mean if you wanted to find the slope visually it might be harder

Answer 20

so it would be better and easier to use the 0,36?

Answer 21

I would suggest that you both choose different points (Teachers might catch on similar points)

Answer 22

@dude

Answer 23

I'm confused on what you said about creating the equation of the line

Answer 24

@Marziman

Answer 25

please help

Answer 26

im so sorry dude my laptop screen went black and i had to restart it e.e

Answer 27

@woolyfrog Do

\(\large \frac{36-0}{0--6}\)

Answer 28

Its okay dont worry

Answer 29

ok thank you

Answer 30

so mine would look like \[\frac{ 11-4 }{ 0- -6 }\]

Answer 31

Close

\(\large \frac{4-0}{11--6}\)

Answer 32

ok I wrote it as 36-0/0--6 what is next

Answer 33

so the answer to this question...in the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.

would be \[\frac{ 4-0 }{ 11--6 }\]

Answer 34

wait no it wouldnt cause they are asking for a table

Answer 35

x | y
--|----
4 | 11
0 | -6

Answer 36

like this? im guessing

Answer 37

We're finding the equation of the line so we can just substitute any number and use it on the table

But yes that table looks good

Answer 38

Solve it wooly

Answer 39

so would this table be the answer to the first question?

Answer 40

x | y
--|----
36 | 0
0 | 6

Answer 41

@dude

Answer 42

wooly dont keep tagging him he will be back you just have to wait tagging him constantly will only frustrate and annoy the person helping e.e we gots dis so dont stress

Answer 43

Hai okay

Answer 44

Oh whoops I have to correct your tables

x | y
-- |----
-6 | 0
11 | 4

and

x | y
--|----
-6 | 0
0 | 36


The directions say you need 4 points, these are only 2

Find the slopes in each

Answer 45

Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.

Answer 46

\(\color{#0cbb34}{\text{Originally Posted by}}\) @woolyfrog
can I use -6,0 to 0,36
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 47

it calls for 2 points and both points contain 2 values i think thats what i means e.e

Answer 48

but i could be wrong x.x

Answer 49

Well I guess that works too but your point 11,4 isn't intersecting the graph
(I think it would be best to include at least 4 points just to be sure)

Answer 50

\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
@woolyfrog Do

\(\large \frac{36-0}{0--6}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 51

.............
T~T fineeeee but how do we get 4 point the airplane can only go in one direction

Answer 52

how do I found 2 more values

Answer 53

Well first solve that so we can just get values easier

Answer 54

Anime

\(\large \frac{4-0}{11--6}\)

Answer 55

36/6

Answer 56

36/6 is right, you can simplify that further

Answer 57

4/17

Answer 58

No

Answer 59

\(\frac{36}{6}=6\)

Answer 60

Hai yes

Answer 61

4-0/11--6= 4/17?

Answer 62

Oh that is Anime's

Answer 63

Yeah

Answer 64

Wooly your equation is

\(y=6x+b\)

Anime your equation is

\(y=\frac{4}{17}x+b\)

Both of you substitute -6 for x and 0 for y

Answer 65

And solve for b

Answer 66

0 = -36 + b

Answer 67

Yes, and what is b?

Answer 68

36

Answer 69

b=24/17?

Answer 70

Yep

wooly = y=6x+36

Anime = y = \(\frac{4}{17}x+\frac{24}{17}\)

Now to find your other points, choose any number and substitute it into x

Answer 71

any number?

Answer 72

would 3 work as x e.e

Answer 73

Yeah any number

3 is good

Answer 74

Uh I okay let me clarify

Any point between -6 and 6

Answer 75

wooly you cannot use -6 and 0 (because you already know those points)

Answer 76

wooly you can use -5,-4,-3,-2,-1, 1, 2,3,4,5,6

Answer 77

do we simplify?

Answer 78

Anime you can use
-5,-4,-3,-2,-1,0,1,2,3,4,5,6

Answer 79

Yep

Answer 80

y=36/17

Answer 81

y=6 2 +36

y= 48

Answer 82

Yep Anime and now do one more number

Answer 83

Which number did you do wooly?

The math looks wrong if you did x=2

Answer 84

like add another number like instead of 3 would 7 work?

Answer 85

I did 2

Answer 86

using 3 = 36/17

Using 7= 52/17

Answer 87

Actually Anime do 5.765

(They are asking for 2 points that intersect)

Are you allowed to use decimals?

Answer 88

ummmm idk tbh

Answer 89

Okay wooly do another point

Answer 90

i mean i can try e.e

Answer 91

You chose slightly hard points to work witb

Answer 92

Uh I'll give you an easier table anime

Answer 93

y=6 3 +36

y= 54

Answer 94

alright e.e

Answer 95

Wooly your table is

x | y
--|----
-6 | 0
0 | 36
2 | 48
3 | 54

Answer 96

wooly, make a separate post so I can help you with your domain and range if you need

Answer 97

Anime we can use points

x | y
-- |----
-3 | 27
2 | 32

Equation of this line is
\(y=x+30\)

Now substitute 2 x values into this

Answer 98

sorry i got confused ....hold on

Answer 99

Okay so I completely changed your table (because I assume you do not like decimals and fractions)

Answer 100

yeah i kinda have a thing against fractions XD but so this whole thing is gone


x | y
--|----
4 | 11
0 | -6

Answer 101

are we starting from scratch now?

Answer 102

or are we keeping these and changing the 2 other points

Answer 103

Yeah just forget those points
x | y
--|----
4 | 11
0 | -6


This is from scratch

Answer 104

x | y
-- |----
-3 | 27
2 | 32

Equation of this line is
\(y=x+30\)

Use this one (it is much easier to work with)

Answer 105

im sorry dude im still confused hold on where are these points on the graph?

Answer 106

ok

Answer 107

So the line is

Answer 108

Okay so now substitute any 2 numbers into x

(I recommend x=0 and x=-1)

Answer 109

Which would be
\(y=(0)+30\)
and
\(y=(-1)+30\)

Answer 110

are we finding the y intercept?

Answer 111

Its the easiest point to find so yes

Answer 112

y=0+30= b=30
y=-1+30=b=29

Answer 113

Yep so your table is

x | y
-- |----
-3 | 27
-1 | 29
0 | 30
2 | 32

Answer 114

alright what is next then

Answer 115

`What is the domain and range of the rainbow? Explain what the domain and range`
`represent. Do all of the values make sense in this situation? Why or why not?`
`What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.`

Make a new post for this, its already long enough

Answer 116

okie