#### Transcript of Rainbow Parabola

**Rainbow Parabola**

GPO

y=x^2+40 y=x^2+40

1) x | y x^2+40=y

0 | 40 (0)^2+40=y

1 | 41 (1)^2+40=y

-1 | 41 (-1)^2+40=y

6 | 76 (6)^2+40=y

-6 | 76 (-6)^2+40=y

Graph

Elizabeth Cho, Tai-in Chung, Grace Choi

Conclusion

Unlike the normal rainbows that have a round edge, the rainbow with the equation: y=x^2+40, will have upside down rainbow.

The Problem

If a rainbow makes a shape of parabola with the formula of y=x^2+40, how would it look like?

Investigate the World

We investigated the world by researching and solving this equation: y=x^2+40. We learned more about the rainbow and we also learned how to review calculations and graph a parabola.

Recognize Perspectives

Communicate Ideas

Take Action

Calculations

We communicated ideas (calculation, graphing, and some facts about rainbow) by presenting to our classmates. As a group, we communicated each others' ideas while we were making this presentation.

How does a rainbow form?

Sunlight is made up of a band of visible wavelengths on the electromagnetic spectrum. When sulight is broken down into its component colors, you can see red, yellow, orange, green, blue and violet colors. Water in the atmosphere can act like a prism refracting the light into the component colors of the rainbow.

We took action by sharing facts about parabola with our classmates. Since we learned some facts about rainbow, we now know how it is formed and when it is made. We also learned how rainbow is like a shape of parabola and what kind of mathematical steps you need to have in order to graph it.

Some Facts about Rainbows

We were able to recognize perspectives by understanding and recognizing the problem in a way we were taught in class. We enjoyed learning about them.

Rainbows occur when it's both raining and the sun is shining simultaneously.

A Rainbow is light refracted through millions of droplets of water

The main colors it gives off are red, orange, yellow, green, blue, indigo and violet.

Double, triple and even quadruple rainbows sometimes occur.

y=x^2+40

1) x | y

0 | 40

1 | 41

-1 | 41

6 | 76

-6 | 76

Upside down Rainbow

It is called 'circumzenithal arcs.'

The normal rainbows form when light refracts through raindrops, mist, or sometimes even sea spray.

The upside down kind however, are caused by ice crystals in the air. They are more common in cold climates.

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