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.

courtesy of texas instruments

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).

Hope this helps

Step-by-step explanation:

The solution and the problem is as follows:

Y= -(-2)^2+36

Y= -4+36

Y=32

Y= -(1)^2+36

y= -1+36

y = 35

The points will be (-2, 32), (1,35)

I will use slope intercept

Formula is f(x) = mx+b

M is y^2-y^1 / x^2-x^1

B will be one of the points, such as 32 or 35

35 = b + 1

Minus the 1 from both sides

B = 34

So f(x) will be f(x) = x + 34

Table of Values

X           Y

-2      32

-135

036

135

232

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

oWhat 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?

The domain is in the x axis.  The range is in the y axis.  The values y make sense.

oWhat are the x- and y-intercepts of the rainbow? Explain what each intercept represents.

The x- and y- intercepts of the rainbow are from the equation.  

oIs the linear function you created with your table positive or negative? Explain.

The graph opens downward which makes the linear function negative. However, the I made the function positive since the airplane is moving up.

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

The solution to the system of equation represents the y and x intercept for the slope intercept. It will also, show where the airplane will be the rainbow.  The two points are (-5, 11) (-4, 20)

•How can graphing be applied to solving systems of nonlinear equations?

This can be applied to finding points that intersect.  

•How can constraints be used to model a real-world situation?

Real world situations can happen when a pilot is look out of the cockpit and notices a rainbow and when he will be able to tell the passenger’s to look out.  Also when he would need to get from point A to B.

ok then what happened.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for