Real World Applications – Algebra I
Designing a Mirror for a Telescope in Space
Astronomers use telescopes to get a good view to see what’s out there in space. For this activity, we’re going to start to look at the importance of designing a mirror for one of these telescopes and represent its design using quadratics.
In this particular activity, we’re given that the circular area of this telescope is 14.12 square meters. This means that the radius is 2.12 meters, and the diameter is 4.24 meters.
If we were to graph this quadratic equation, we will have the following:
Now, just by looking at this graph, it doesn’t have the shape of a symmetrical mirror for an astronomer. Why not?
We know that the radius of the mirror is 2.12 meters, and the diameter is 4.24 meters. Let’s change our graph so that our graph only reaches a maximum width, or horizontal distance, of 4.24 meters.
Much better! What observations can you make about this graph and the mirror of the telescope?
Let’s dig a little bit deeper into the Algebra of this quadratic equation and analyze what the discriminant means.