Posted in Algebra, Calculus, Computer Science, Education, Geometry ', Math Tutoring, Mathematics, Pre-Calculus, Statistics, Studying, Tutoring

Why do I Have to Learn this: Parabolas?

As tutors and educators, we all bring different areas of expertise and knowledge to the table.  Here at Oxford Tutoring, we can assist all varieties of learners from Kindergartners learning phonics to a Seniors in High School applying to the college of his or her dreams.  Specifically, Oxford Tutoring provides Math tutoring, English Language Arts tutoring, Science tutoring, SAT and ACT Test Prep, and more.  Suffice it to say, each of us has tutored all types of students in all types of subjects.  Despite differences in our expertise, our students, and our experiences, one thing we have almost all been asked by our students is, “Why do I have to learn this?”  A frustrated student will come across a concept like the mechanics of grammar or Algebraic functions and wonder how on earth this information could ever prove useful outside of the classroom or in their lives.  In response to this very common question, we have started a blog series that will help students apply their education to their world.

In this first entry of Oxford’ Tutoring’s “Why do I Have to Learn this?” series, we will explore the link between the math of parabolas and it’s applications in the real world.


You can sum up the reaction I get when I tell my students that math shows up in the real world with the word incredulity.  They all have seen “application problems” in their Math books, but are unable to believe that these scenarios could be possible in the real world because it is within the context of their Math book.  However, our tutors present applications of Math to a student, one-on-one in their tutoring sessions based on what is relevant to the student. The fact that it comes from the mouth of another human, a Math tutor, takes a subject that students often find bland, and injects it with new life.

Parabolas are one of the first places that students can get a taste of where math meets the world.  Students quickly understand that a parabola (the concept usually taught in Algebra 1 and Algebra 2) is the basis for the “paraboloid,” a three-dimensional figure similar to a bowl they ate cereal out of that morning with the same focus (the fixed point inside the parabola) and axis of symmetry (the vertical line that divides the parabola into equal halves).

Parabola to Paraboloid

By making a connection between the equation of a parabola and a real world shape (the parabaloid), students are able to find the missing link between the Mathematics of the classroom and real world objects. In so doing, they can conceptualize complex concepts they might otherwise detest.  Because students do not get a taste of this in school, it has not yet sunk in the equation of parabola is the basis for the technology behind car headlamps, satellite television, internet access and optical light telescopes to name a few.  To clarify, parabolas and paraboloids have the same property – if we treat the figure as a reflective surface (essentially a mirror) two equal and opposite events can occur:

  1. Anything that comes in parallel to the axis of symmetry gets reflected to the focus
  2. Anything that comes out of the focus and gets reflected comes out parallel to the axis of symmetry

While these events seem extremely complex for a student just tackling Algebra 1 or Algebra 2, just consider the aforementioned examples and how they connect to these events:

  • Car headlamps, that allow us to drive at night (an example of event 2), function because the lightbulb sits on the focus, and the strong beam in the distance is the light coming out parallel to the axis of symmetry.


  • Satellite television and internet access (an example of event 1) function because the satellite in orbit is far enough away that any signal received is essentially parallel, and the receiver is at the focus point.

            Satellite Dish

  • Optical light telescopes (an example of event 1) function because of a paraboloid mirror that is a key part of the assembly, similar to that of a satellite television dish.


Generally, after discussing and viewing a few drawings on these ideas, the students start to realize that not only is math in underlying ideas in the real world, but it is also providing students a direct benefit, be it the enjoyment they get from star gazing, the usefulness of internet access, or the safety it provides them as they drive home from a late tutoring session.  It is this realization that often spurs the student onward through difficult content and makes that content memorable and meaningful, the seed for future scientific pursuits.

Meet the author:  Jason, a Math and Computer Science Instructor has been tutoring with Oxford Tutoring for over nine years.  Utilizing the student’s existing knowledge and a touch of humor, Jason strives to remove students mental barriers between themselves and the difficult, technical materials.  He combines his years of tutoring experience and expertise in the fields of Math and Computer Science to give his students the tools they need to succeed in these challenging classes.

Email us to book us session with an Oxford Tutoring Math and Science tutor.

Or give us a call at (949) 681-0388!

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Oxford Tutoring specializes in K-12 tutoring in English, mathematics, science and test preparation. We provide skill building and homework help in private, one-on-one sessions coordinated with our student’s classroom programs, but focused on the way in which each student learns. Working to better each student’s academic success, Oxford Tutoring personalizes our tutoring approach to best meet the education needs of our students.

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