10-2 Conics: parabola

Allie R, icm

problem 1: Put the following into standard form:  y²-6y+9-x=5

step 1: put the x variable on the other side of the = sign from they y variable

y2-6y+9=x+5

Step 2: simplify the squared term

(y-3)²=x+5

Now it is in standard form

Problem 2: Graph the parabola x+5=(y-3)²

Step 1: define the points: vertex, foci, axis of symmetry, directrix, latus rectum

Vertex=look at the original equation in standard form where the x is located, if x is by itself then x=o but since x+5 you put it equal to zero and subtract 5 so that you get x=-5. then you do the same thing for the y where (y-3) so y=3. therefore the vertex point of this parabola is (-5,3).                                                                                                                                                                                       Foci= a point that is on the same line as the vertex inside the parabola. look at the parabola. first you have to determine whether the direction of the parabola is facing up, down, left or right. If the problem is x=y² then it goes to the right, x=-y² then it goes to the left, y=x² goes up and y=-x² then the direction is down. Since the problem is x=y² then the direction is to the right. in this case to find the foci you add the square root of the value below the squared term to the x value since the shape of this parabola is to the right. therefore the focus point is (-4,3).                                                                                                                            Directrix= since the focus distance is 1 then to find the directrix all you have to do is go the same distance as the foci from the vertex but in the opposite direction. this line is x=-6 latus rectum= the distance from side to side in the same line as the foci on the parabola. the equation for this is 4a. a is the number in front of the squared term. so 4(1)=4. therefore the distance of the lr=4                                                                                                                                       Axis of symmetry= this is the line that splits the parabola in half so that it is symmetrical on both sides. to name this all you have to do is draw a line through the vertex to split it and name what line it is. in this case aos is y=3.

Step 2: Graph all the information from above

The red represents the vertex point, the blue represents the points for the distance of the LR, the purple represents the focus point, the orange represents the AOS, the green is the parabola, and the pink is for the directrix. 

"Grant that I might give without remembering and receive without forgetting" -quote from calendar 2003. this quotation deals with the character education trait of "Self-discipline" because you have to discipline yourself so that you can achieve the ability to be a giving person without holding your kindness to other people and for when you receive something to be eternally grateful!

http://www.mste.uiuc.edu/dildine/sketches/parabola.htm

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