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http://prntscr.com/nlaht4

 May 6, 2019
 #1
avatar+100519 
+1

1.  y  = x^2 - 8x + 12

 

y - 12  =  x^2 - 8x           complete the square on x

 

y - 12  + 16  =   x^2 - 8x + 16      simplify

 

(y + 4)  = (x - 4)^2

 

We have the form  (4p)(y - k) = (x - h)^2

 

The vertex  =   (h, k) =   ( 4, - 4)

Axis of symmetry    x  = 4

p  = (1/4)

The focus  =  ( 4 , - 4 + p)  =  ( 4, - 4 + 1/4)  =  ( 4, -15/4)

The directrix  =  y = (k - p)  =   - 4 - 1/4   =   -17/4

 

Here's a graph : https://www.desmos.com/calculator/am3svgafgw

 

cool cool cool

 May 6, 2019
 #2
avatar+100519 
+1

x = 2y^2 -8y + 3

 

x - 3  = 2(y^2 - 4y)         complete the square on y

 

x - 3 + 8  = 2(y^2 - 4y + 4)       simplify

 

(x + 5)  = 2(y - 2)^2 

(1/2)(x + 5)  = (y - 2)^2        

 

Vertex  =  ( -5, 2)

We have the form   (4p)(x + 5) = (y - 2)^2

4p = 1/2

p = 1/8

 

This parabola opens to the right

The axis of symmetry is y = 2

The focus  =  ( -5 + p , 2)  = (-5 + 1/8, 2)  = ( -39/8, 2)

The directrix is    x = -5 - p  =  -5 - 1/8  =  -41/8

 

 

cool cool cool

 

Here's the graph :  

 May 6, 2019
 #3
avatar
0

Thank youuuu!

 May 6, 2019

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