Lukas'+choice

A rainbow is a spectrum of light made visible by moisture in the air. After rainfall if the sun breaks from behind the clouds while the clouds still hold moisture than an optical illusion takes pace and we see a rainbow. While it may appear that a rainbow touches the ground (in fact several myths and fables refer to it) science has proven that a rainbow (talking on large scale not sprinkler scale) can only exist high up in the troposphere where the moisture still resides. Rainbows take shape in the air because the light of the sun hits the water droplets ad is reflected in them causing the famous primary colored rainbow.

Interestingly, the spectrum of light that we call a rainbow is just one of many spectrums, reflections, or images of light that are caused by the sun, but unfortunately some are invisible to the human eye. (or you can't see them from the ground!) An less known example of things our eyes can't see well is something called a moonbow. It is not commonly heard of but it works in much the same way. The light from the sun reflects off the moon and on nights when the light is strong and it has rained a band of white light can be faintly seen. However most people have never seen one, and most who have dismiss them for the are not as beautiful as out traditional rainbow. A rainbow actually has no fixed place in the sky, where it is is relevant to the observer. However the above is a sample of were it could be The equation of the above parabola in standard form is: y=-0.0009x^2+1.3333x+500. In vertex form it is:y-543.8=-0009(x-740.72)^2. In factored form it is: y=-0.0009(x-1790.7)(x+309). The discriminant of this parabola is 1.89. I found the discriminant by working out the equations above and to the left. My discriminant is not factorable over the integers as it is not a whole number. The discriminant tells us if the numbers are rational numbers. There are two x-intercepts for this parabola. They are: 1790.7, and -309. Like everything else about a rainbow you could not find them if it were not for the equations. the x-intercepts represent the points where the rainbow would touch the ground if it did. Using these equations and the graph I chose a equation to test my parabola. I decided to test the formula with asking it using the quadratic formula what the y would be if x=800. Both the equations and the graph decided on the points: (800,250), and (800,1250). Thus I checked my work, I will say just one more time... This parabola does not touch the ground, but if it did the above would be its x-intercepts, factored form, and discriminant. My Vertex for the made up rainbow above is (750,1000). I found this vertex when I created the parabola from where are rainbow might appear. If you did not look at the graph above, or at the equation, you would have no way of knowing the vertex because a rainbow has no fixed place in the sky and as such has no fixed vertex. The parabola graphed above is a maximum and opens up just like every other rainbow that is not artificially created. The vertex signifies the point where the rainbow is the highest in the sky. Need I repeat that that point is not fixed? The equation for the axis of symmetry is X=750. The y-intercept of this Parabola is (0,500). Like the vertex I found the y-intercept after I created the graph, and also like the vertex there is no other way to find it. The y-intercept signifies one of two start points for the rainbow graphed and explained by me above. Now for conic sections. A parabola is properly defined as a conic section. The section is the right conical section. The only thing that parabolas really have in common with cones, besides how they hep us understand parabolas, is that if you take a paper thin slide out of the right conical surface you get a parabola. For more on cones and parabolas visit my discussion of defining parabolas.