Subject: parabolas

My name is Michelle and I am a 10th grade student in algebra 2 w/ analysis. I am doing a report on parabolas and I need to know what the general equation is. I've looked in books and keep finding different ones! I also need to know how they can be used in nature.

Thank you so much for your time. I really appreciate it!

- Michelle

Hi Michelle,

The meaning of "the general equation of a parabola" is not the same for everyone. Usually the first time that students see the term "the general equation of a parabola" the teacher is thinking of a parabola that opens upwards with its vertex at the origin. Thus the focus has X-coordinate 0 and Y-coordinate some positive value. If we use the notation that the focus is at (0,p), where p is positive, then the equation of the parabola is y=x^2/(4 p). Some texts later say that the "general parabola" has equation y = a x^2 + b x + c. For different choices of a, b and c, as long as a is not zero, you can get a parabola that open upwards or downwards that may or may not have its vertex at the origin. If you have a graphing calculator of computer software that will plot graphs it is fun to select values for a, b and c and plot the graph. Take values where you can factor the expression. For example y = 2x^2+5x-12 = (2x-3)(x+4). Plot it. Now change the values of 2, -3 and 4 one at a time and plot each time. Change their signs and plot.

A place where you can find a development of the equation y=x^2/(4 p) and a note on a practical application of the parabolic shape is a resource at Math Central called Why are satellite dishes parabolic?

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