+0  
 
0
252
2
avatar+259 

Question 1)

Question 2)

Question 3)

Thanks so much for always helping 

 May 5, 2018
 #1
avatar+98061 
+1

1.  y  = -1/4x^2 + 4x  - 19

 

The x coordinate of the vertex  is given by   -4 / (2 * -1/4)  =  -4 / (-1/2)  =   -4 * -2    =  8

And the y coordinate is given  by :

-1/4 (8)^2  + 4(8)  - 19  =

-16  + 32   - 19

-3

 

So....the vertex  is  (8, -3)

 

Here's a graph : https://www.desmos.com/calculator/z76eahtb61

 

2. The center of the circle  is  ( 1, 4)   and the radius  is 8

 

So we have

 

(x - 1) ^2   + ( y - 4)^2   = 8^2        expand and simplify

 

x^2 - 2x + 1  + y^2  - 8y + 16  = 64

 

x^2 + y^2  - 2x - 8y  + 17  = 64       subtract 64 from both sides

 

x^2  + y^2  -2x - 8y - 47   =  0 

 

 

 

3.  We have    y   =  1/8 x^2 + 4x + 20

 

We want to complete the square  on x

 

y = (1/8)  (x^2  + 32x + 160)

 

Take  1/2 of 32  = 16....square it  = 256....add and subtract it within the parentheses

 

y  = (1/8)  (x^2 + 32x  + 256   + 160   - 256)       factor the first three terms, simplify the last two

 

y = (1/8) [ (x + 16)^2  - 96 ]       apply the  1/8   over both terms in the parentheses

 

y  = (1/8) (x + 16)^2 - 12

 

(y + 12)  = (1/8)(x + 16)^2     multiply both sides by 8

 

8( y + 12)  = (x + 16)^2

 

The vertex  is at  (-16, -12)

 

In the form

 

4p ( y - k)  = (x - h)^2

 

4p  = 8

 

So....p  = 2

 

And the focus is given by

 

(-16 ,  -12 + p)   =    (-16, -12 + 2)   =   (-16, -10)

 

Here's the graph  :  https://www.desmos.com/calculator/cgsvcjy0ny

 

 

 

cool cool cool

 May 5, 2018
 #2
avatar+259 
+1

thank you so much CPhill you always help me so much!

Johnnyboy  May 5, 2018

16 Online Users

avatar
avatar
avatar