9.1-9.3 Quiz (Conic Sections)-KEY 1. Complete the square. 2. Use

9.1-9.3 Quiz (Conic Sections)-KEY
1. Complete the square.
y 2  6 y  8 x  25
y 2  6 y  ____  8 x  25  ____
y 2  6 y  9  8 x  25  9
 y  32  8 x  16
 y  32  8x  2
2. Use Min Lee’s Conjecture
I will choose x=3 and x=1 (one unit to the right of the given point and one unit
to the left of the given point). Now substitute these x-values into our equation.
2
x  3; y  23  18
x  1 : y  21  2
2
Now, find the slope between the points (3, -18) and (1, -2)
 2   18  16  8
m
1  3
2
Next, use y  mx  b . Substitute your values. You must use the original
point (2, -8). Solve for b.
 8  8  2  b
 8  16  b
8b
 y  8 x  8
0  8 x  8
Lastly, find the x-intercept of your line:
 8  8 x
1 x
1, 0 
3. Complete the square.
y 2  16 x  16
y 2  16( x  1)
4 p  16
p  4 so you must move 4 units left of vertex
 directrix : x  3
4. Sketch a diagram to represent the situation.
Use:
(0, h)
(15, 22)
(39, 0)
5.
25 y 2  150 y  144 x 2  576 x  3951

25 y



25 y 2  6 y  ____  144 x 2  4 x  ____  3951  ____  ____
2



 6 y  9  144 x  4 x  4  3951  225  576
2
25 y  3  144x  2  3600
2
  2,  3
2
6. Sketch a diagram; Note: p = 1. Use  y  k   4 px  h
Substituting values we get:
 y  12  41x  3
2
y 2  2 y  1  4 x  12
 y 2  2 y  4 x  13  0
x  h 2   y  k 2
1
b2
a2
From diagram, we know a=5, b=2 and center = (3, -2). Plug in values.
x  32   y  22  1
4
25
7. Sketch a diagram; Note: Vertical Major Axis. Use
8. Standard form of Conics: Ax 2  Bxy  Cy 2  Dx  Ey  F  0
Note: A=-3, B=0, and C=0. Substitute these values into Discriminant:
B 2  4 AC
02  4 30
0
 Parabola
A faster way to arrive at this answer is to notice that only one of the variables
is squared (namely, x 2  term ); indeed it’s a parabola when this happens.

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