+0  
 
0
50
2
avatar+173 

Question 1)

Question 2)

Question 3)

Thanks so much for always helping 

Johnnyboy  May 5, 2018
Sort: 

2+0 Answers

 #1
avatar+86643 
+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

CPhill  May 5, 2018
 #2
avatar+173 
+1

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

Johnnyboy  May 5, 2018

12 Online Users

New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy