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A teacher's guide to lectures on parabolas.

Once again, when you start, don’t tell them we’re doing parabolas! Tell them we’re going to create another club. This time the requirement for membership is: you must be exactly the same distance from the point (0,3) that you are from the line y = -3 . For instance, the point (3,3) is not part of our club—it is 3 units away from (0,3) and six units away from y = -3 .

Now, let them work in groups on “All the Points Equidistant from a Point and a Line” to see if they can find the shape from just that. If they need a hint, tell them there is one extremely obvious point, and two somewhat obvious points. After that they have to dink around.

When all or most groups have it, go through it on the blackboard, something like this. The extremely obvious point is the origin. The “somewhat” obvious points are (-6,3) and (6,3). Show why all those work.

Now, can any point below the x-axis work? Clearly not. Any point below the x-axis is “obviously” (meaning, after you show them for a minute) closer to the line, than to the point.

So, let’s start working up from the origin. The origin was in the club. As we move up, we are getting closer to the point, and farther away from the line. So how can we maintain equality? The only way is to move farther away from the point, by moving out. In this way, you sketch in the parabola.

Now, you introduce the terminology. We’re already old friends with the vertex of a parabola. This point up here is called the focus. This line down here is the directrix. The focus and directrix are kind of like the center of a circle, in the sense that they are central to the definition of what a parabola is, but they are not themselves part of the parabola. The vertex, on the other hand, is a part of the parabola, but is not a part of the definition.

The directrix, of course, is a horizontal line: but what if it isn’t? What is the directrix is vertical? Then we have a horizontal parabola. Of course it isn’t a function, but it’s still a shape we can graph and talk about, and we have seen them a few times before. If you have time, work through x = 4 y 2 8 y .

Homework:

“Homework: Vertical and Horizontal Parabolas”

Questions & Answers

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4
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x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
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Need help solving this problem (2/7)^-2
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x+2y-z=7
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what is the coefficient of -4×
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-1
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the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
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An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
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lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
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12, 17, 22.... 25th term
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12, 17, 22.... 25th term
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Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
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find the 15th term of the geometric sequince whose first is 18 and last term of 387
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salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
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Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Source:  OpenStax, Advanced algebra ii: teacher's guide. OpenStax CNX. Aug 13, 2009 Download for free at http://cnx.org/content/col10687/1.3
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