- A parabola is a symmetrical, curved, U-shaped graph.
- The equation of a parabola graph is y = x²
- Parabolas exist in everyday situations, such as the path of an object in the air, headlight shapes and the wire of suspension bridges.
The education officer at Jodrell Bank describes how parabolas explain the structure and shape of the Lovell Telescope
I'm the education officer here at Jodrell Bank Discovery Centre.
So, Jodrell Bank is the site for the Lovell Telescope which is the third largest steerable telescope in the world.
We look at distant galaxies. We're also looking at objects called pulsars, which are the cores of exploding stars which are rapidly rotating and all sorts of other stuff in space as well.
The Lovell Telescope, as well as the majority of the telescopes here at Jodrell Bank, are actually a 3D model of a parabola.
So, a parabola is your normal 2D shape that you'll actually get and you'd draw on paper but, if you want to make it into a 3D shape, you'll have it as a paraboloid.
And that's actually what the telescopes are, they're paraboloids.
The simplest equation for a parabola is actually y = x².
Now, if I start off with a x-y graph and I draw a parabola, it would cross at zero and then come back up.
Now, that is the 2D shape of our telescope. What we really want is for radiation coming down from space to actually enter into somewhere called the focus, which is at the very middle of it.
If I wanted to find out where the receiver is, I'd have to use a separate equation. F, which is our focus, is equal to a quarter.
Now, that is actually telling me exactly where the focus would be. So where I'd actually place my receiver for our telescope would be at that focus, where f is equal to a quarter.
Parabolas in graphs
The equation of a parabolic graph is y = x² and all quadratic graphs have a line of symmetry which passes vertically through the minimum or maximum point.
The minimum point is the minimum y value that the parabola reaches.
The maximum point is the maximum y value that the parabola reaches.
The symmetry of the parabola is created because each x value is squared. Whatever value we square, it will always result in a positive value, regardless of whether it is positive or negative to begin with.
For example
-1.2² = 1.44
2.5² = 6.25
Graphs of y = x² + n can be easily drawn by moving the parabola n places up or down the y axis.
y = x² + 6 moves the parabola 6 places up the y axis.
y = x² – 7 moves the parabola 7 places down the y axis.
Parabolas in real life
In the video, the 2D curve of the Lovell Telescope dish is a parabola. It is this shape and structure that allows the telescope to gather incoming radio waves.
When the telescope is pointed towards a radio source in the sky, waves arriving from the source are intercepted by the bowl and reflected from its steel surface into the focus box mounted on top of the central tower.
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