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.
Create an equation. Use the graph below to create the equation of the rainbow parabola.

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- anonymous

y = a(x - p)(x - q)
p and q are the zeros of the parabola, -6 and 6
y = a(x + 6)(x - 6)
Substitute third point (0, 36) into the above equation to solve for a.

- anonymous

@peachpi so i plug 0 in for x and then 36 i plug it in where the y is?

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- anonymous

yes

- anonymous

is the answer a=-1? @peachpi

- anonymous

yes

- anonymous

can you help me on the next question please?? @peachpi

- anonymous

if i can

- anonymous

Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.

- anonymous

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

- anonymous

Pick two points that the parabola goes through and then write the equation of the line that connects them.

- anonymous

What points would be the easiest?

- anonymous

any two points where gridlines meet. Or if you have a graphing calculator you can pick points with integers or simple fractions

- anonymous

5,5?

- anonymous

i mean 5,10

- anonymous

The line has to intersect the parabola twice AND move upward.
You need a lower point on the left side and a higher point on the right side
|dw:1433865603177:dw|

- anonymous

You chose 5 on the right, but that won't really work with moving upward. Try -5 on the left, and plug it into the equation we found above to find the y-coordinate.

- anonymous

i am so confused like idk where to even start.

- anonymous

when you plug -5 into the equation we got for the first part, what do you get?

- anonymous

what do i plug it in for? which variable

- anonymous

for x. to solve for y

- anonymous

so y=-1(-5+6)(-5-6)? then solve?

- anonymous

yes

- anonymous

y=11?

- anonymous

yes. Now pick an x-value on the right side and do the same thing to get the other point.
|dw:1433866189861:dw|

- anonymous

-4?

- anonymous

yes you can use -4

- anonymous

what do i plug that in for?

- anonymous

x

- anonymous

y=20

- anonymous

ok. great :)
so now you want to find the equation of the line through (-5, 11) and (-4, 20)

- anonymous

Start by finding the slope

- anonymous

what is the formula again? sorry!

- anonymous

|dw:1433866705637:dw|

- anonymous

9/1

- anonymous

yes, or just 9. So y = 9x + b.
Plug in either of the 2 points to solve for b

- anonymous

i can plug in 11 for y or x?

- anonymous

if you plug in 11 for y, then use -5 for x

- anonymous

b=56???

- anonymous

yes

- anonymous

so how do i answer the question in paragraph form?

- anonymous

sorry, which question?

- anonymous

which question did i just do all that work for question 2?

- anonymous

that was for the question with the table. The equation for the line is y = 9x + 56 and you have two points on it. Find any two other random points
|dw:1433867320239:dw|

- anonymous

ok so that is all for #2?

- anonymous

yes.

- anonymous

I actually have to go. Sorry I can't help anymore

- anonymous

the domain of the rainbow is [-6,6] and the range is [0,36] and it's just the shape of the rainbow. The linear function is increasing and positive and represents the path of the drone. the solutions are (-5,11 and (-4,20) and they are where the drone passes through the rainbow

- anonymous

You are awesome thank you!

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