grr

- anonymous

grr

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- katieb

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- Michele_Laino

we know that your function has to be a polynomial of degree 2
from your drawing we see that x=6 and x=-6 are two zeroes of the requested polynomial

- anonymous

Oh! So would it be -1(x+6)(x-6) ??

- Michele_Laino

the simpler polynomial which satisfies those requisites is:
\[y = \left( {x - 6} \right)\left( {x + 6} \right)\]
even if, we have to check if my function contains the point (0,36)
does my function pass at point (0,36)?

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## More answers

- Michele_Laino

yes! that's right!

- anonymous

Ok so then I got -x^2+36?

- Michele_Laino

correct!

- anonymous

There is a 2nd part to this question, I'm not getting

- anonymous

I know, I'm lost too:)

- Michele_Laino

you have to create a table for a straight line like this one:
|dw:1438706644480:dw|

- Michele_Laino

step#1 please chose two point on your rainbow

- Michele_Laino

oops.. choose*

- anonymous

um 3?

- Michele_Laino

you have to choose 2 values for x-coordinate

- Michele_Laino

between -6 and 6

- anonymous

oh okay then 5

- Michele_Laino

x1=5 and x2=?

- anonymous

11?

- Michele_Laino

no, your value has to be less than 6 and grater than -6

- Michele_Laino

x=5 is right! the other value can be x=2

- Michele_Laino

what do you think?

- anonymous

yes, i agree

- Michele_Laino

ok!

- Michele_Laino

now we have to compute the corresponding y-value, so, if x=5
then:
y=-5^2+36=-25+36=11

- Michele_Laino

whereas if x=1, then:
y=-1^2+25=...?

- anonymous

I see, I see:)

- anonymous

24

- Michele_Laino

sorry if x=1, then:
y=-1^2+36=35
we have these points:
(1,35) and (5,11)

- anonymous

I agree:)

- anonymous

so then we would have to make a chart, and another function right?

- Michele_Laino

now:
step#2
we have to write the equation of the straight line which passes at points
(1,35) and (5,11)

- Michele_Laino

for example we can use this equation:
\[\Large y - 35 = m\left( {x - 1} \right)\]
where:
\[\Large m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{11 - 35}}{{5 - 1}} = ...?\]

- anonymous

-24/4

- anonymous

-6

- Michele_Laino

yes!

- Michele_Laino

so, what is the equation of your straight line?

- anonymous

um y=6x+1?

- anonymous

i mean y=-6x

- Michele_Laino

we have to substitute our value of m, into my equation above:
\[\Large y - 35 = - 6 \cdot \left( {x - 1} \right)\]

- Michele_Laino

please, simplify

- anonymous

y-35=-6x+6

- Michele_Laino

so:
y=...?

- anonymous

y=-6x-29

- Michele_Laino

I got:
Y=-6x+41 am I right?

- anonymous

yes. whoops:)

- Michele_Laino

ok! Now the exercise asks you at least four points

- Michele_Laino

you have already two points:
(1,35) and (5,11)

- Michele_Laino

so you have to choose another 2 values for x, and compute the corresponding value for y. Please keep in mind that x has to be greater than -6 and less than 6

- anonymous

what about 2?

- Michele_Laino

whit those four points you have to create a table like this:
|dw:1438708104245:dw|

- Michele_Laino

ok! x=2 is good, so:
y= -2^2+36=-4+36=...?

- anonymous

32

- Michele_Laino

so the third point is:
(2,32)

- Michele_Laino

now, we can choose x=-3

- Michele_Laino

what is y?

- anonymous

45

- Michele_Laino

I got this:
y=-(-3^2)+36=-9+36=27

- anonymous

yes<3

- anonymous

Yayyy! We did it! So just to make sure, the 2nd equation is y=-6x?

- Michele_Laino

so, the requested table is:
|dw:1438708531419:dw|

- Michele_Laino

the second equation is:
\[\Large y = - 6x + 41\]

- anonymous

oh, so is it possible that we could have plug the points into that equation to get the points too?

- Michele_Laino

please wait

- Michele_Laino

I have made an error, at x=2 we have to compute the value of the y-coordinate of the line, namely:
\[\Large y = - 6 \cdot 2 + 41 = ...\]

- Michele_Laino

similarly at x=-3:
\[\Large y = - 6 \cdot 3 + 41 = ...\]

- anonymous

29

- anonymous

so can we draw the chart again and see?

- Michele_Laino

ok! so we got these points:
(2,29) and (-3,23)

- anonymous

|dw:1438708966376:dw|

- anonymous

what would the domain/range be?

- Michele_Laino

that's right!

- Michele_Laino

the domain of the direction of the drone, it is all the real line

- anonymous

so would the domain be -6 and 6 then?

- Michele_Laino

it is the domain of the rainbow, I think

- anonymous

ohhh

- anonymous

Thanks for all your help!!!!! :D

- Michele_Laino

please wait, I have made another error, the fourth point is:
(-3,59)

- anonymous

Good thing you caught that!

- Michele_Laino

since we have:
\[\Large y = \left( { - 6} \right) \cdot \left( { - 3} \right) + 41 = 18 + 41 = 59\]

- Michele_Laino

the domain of the rainbow is the subsequent interval:
(-6,6)
whereas its range is (0,36)

- anonymous

what would that represent?

- Michele_Laino

the range is the set af possible values of the function -x^2+36 when
x is inside the domain

- anonymous

Is the linear function you created positive or negative? Explain.

- Michele_Laino

I think that it represents the possible Rainbow heights with respect to the Earth's surface

- Michele_Laino

the linear function which we have created has a negative slope, so I think it is negative

- anonymous

What are the solutions or solution to the system of equations created? Explain what it or they represent.

- anonymous

thanks so much:)

- Michele_Laino

the requested solution is given by the coordinates of the intersection points, namely:
(1,35) and (5,11)

- Michele_Laino

:)

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