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

yes! that's right!
Ok so then I got -x^2+36?
correct!
There is a 2nd part to this question, I'm not getting
I know, I'm lost too:)
you have to create a table for a straight line like this one: |dw:1438706644480:dw|
step#1 please chose two point on your rainbow
oops.. choose*
um 3?
you have to choose 2 values for x-coordinate
between -6 and 6
oh okay then 5
x1=5 and x2=?
11?
no, your value has to be less than 6 and grater than -6
x=5 is right! the other value can be x=2
what do you think?
yes, i agree
ok!
now we have to compute the corresponding y-value, so, if x=5 then: y=-5^2+36=-25+36=11
whereas if x=1, then: y=-1^2+25=...?
I see, I see:)
24
sorry if x=1, then: y=-1^2+36=35 we have these points: (1,35) and (5,11)
I agree:)
so then we would have to make a chart, and another function right?
now: step#2 we have to write the equation of the straight line which passes at points (1,35) and (5,11)
for example we can use this equation: \[\Large y - 35 = m\left( {x - 1} \right)\] where: \[\Large m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{11 - 35}}{{5 - 1}} = ...?\]
-24/4
-6
yes!
so, what is the equation of your straight line?
um y=6x+1?
i mean y=-6x
we have to substitute our value of m, into my equation above: \[\Large y - 35 = - 6 \cdot \left( {x - 1} \right)\]
please, simplify
y-35=-6x+6
so: y=...?
y=-6x-29
I got: Y=-6x+41 am I right?
yes. whoops:)
ok! Now the exercise asks you at least four points
you have already two points: (1,35) and (5,11)
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
what about 2?
whit those four points you have to create a table like this: |dw:1438708104245:dw|
ok! x=2 is good, so: y= -2^2+36=-4+36=...?
32
so the third point is: (2,32)
now, we can choose x=-3
what is y?
45
I got this: y=-(-3^2)+36=-9+36=27
yes<3
Yayyy! We did it! So just to make sure, the 2nd equation is y=-6x?
so, the requested table is: |dw:1438708531419:dw|
the second equation is: \[\Large y = - 6x + 41\]
oh, so is it possible that we could have plug the points into that equation to get the points too?
please wait
I have made an error, at x=2 we have to compute the value of the y-coordinate of the line, namely: \[\Large y = - 6 \cdot 2 + 41 = ...\]
similarly at x=-3: \[\Large y = - 6 \cdot 3 + 41 = ...\]
29
so can we draw the chart again and see?
ok! so we got these points: (2,29) and (-3,23)
|dw:1438708966376:dw|
what would the domain/range be?
that's right!
the domain of the direction of the drone, it is all the real line
so would the domain be -6 and 6 then?
it is the domain of the rainbow, I think
ohhh
Thanks for all your help!!!!! :D
please wait, I have made another error, the fourth point is: (-3,59)
Good thing you caught that!
since we have: \[\Large y = \left( { - 6} \right) \cdot \left( { - 3} \right) + 41 = 18 + 41 = 59\]
the domain of the rainbow is the subsequent interval: (-6,6) whereas its range is (0,36)
what would that represent?
the range is the set af possible values of the function -x^2+36 when x is inside the domain
Is the linear function you created positive or negative? Explain.
I think that it represents the possible Rainbow heights with respect to the Earth's surface
the linear function which we have created has a negative slope, so I think it is negative
What are the solutions or solution to the system of equations created? Explain what it or they represent.
thanks so much:)
the requested solution is given by the coordinates of the intersection points, namely: (1,35) and (5,11)
:)

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