10.2 – Parabolas
May 15th, 2011 by corricelli
Hello,
Please use this page to post questions/comments/concerns/feedback related to Chapter 10, Section 2.
Feel free to view the following Khan Academy Videos for an overview of the most crucial concepts. There are two here – just click on the second one to see it!
Video: http://www.khanacademy.org/video/parabola-focus-and-directrix-1?playlist=Algebra
Looking for an intro to conic sections? Click here.
What about a few pdf files (with answers) about parabolas? Try this: Graphing and Properties of Parabolas or maybe this: Equations of Parabolas
Happy Parabola-ing,
Mrs. Corricelli
Hey guys,
for #57 i have found the vertex, and have gotten the standard form equation of x^2 = (y-2) but the answer has a coefficient of -8 in front of the parentheses part. I think it has something to do with p which i found as 3, but i’m missing the big picture. where does the -8 come from?
Haley and Teammates,
The vertex is at (0,2) and the directrix is at y=4 so the parabola is facing down (thus the negative). The distance from the vertex to the directrix is 2 so p=2.
Hope this helps,
Mrs. Corricelli
Hey,
so I couldn’t find the page for 10.8, so I hope someone gets this. I am sort of confused on how to use symmetry to help graph polar equations. It says to use substitution to see which symmetry applies. But I tried that in #31 on the homework. Calc Chat says the graph is symmetric with respected to theta = pi/2, but I didn’t get this. I’m not sure if i am doing the arithmetic incorrectly or just not understanding the concept.
Hello Laura,
Do not use the symmetry approach as dictated in the book. Use your knowledge of trigonometric functions as we did in class. Sketch to get a general pattern; look for Special Polar Graphs as specified on p. 787.
As for number 31, r=4(1+sin(theta)) = 4 + 4sin(theta), a limacon with a/b = 1 so it is a cardioid. sin(theta)’s max value will occur when theta = pi/2 (since that will make sin(theta) = 1). Sooo 4 + 4sin(theta)’s max value is also there. Similarly, sin(theta)’s minimum value is -1, when theta = 3pi/2. So that is this equation’s minimum value too. This makes this shape an upside-down heart, symmetric with the “y-axis” (line containing the minimum and maximum). It crosses the x-axis at 4 and -4.
Remember you can use your graphing calculator too. Set the mode to degrees and polar. Zoom standard and zoom square. Trace to see these points. Experiment and have fun! Look for patterns! What if the 4 were negated? What if cosine, instead of sine, were used?
Also check out this link to an applet that allows you to plot polar graphs: http://www.ies.co.jp/math/java/calc/sg_kyok/sg_kyok.html.
Hope this helps,
Mrs. Corricelli