+0  
 
0
275
2
avatar

what the descride transformation (3,1),(0,-5),(-4,-2)

off-topic
Guest Apr 23, 2017
 #1
avatar+7318 
0

what the descride transformation (3,1),(0,-5),(-4,-2)

 

A graph through the three points may be a circle or a second-degree parabola, 3rd degree or higher degree.

 

Circle:

 

\(x_M=\frac{x_1+x_2+x_3}{3}=\frac{3+0-4}{3}\\x_M=\frac{7}{3}\)

 

\(y_M=\frac{y_1+y_2+y_3}{3}=\frac{1-5-2}{3}\\y_M=-2\)

 

\(r=\sqrt{(x_M-x_1)^2+(y_M-y_1)^2}\)

\(r=\sqrt{(\frac{7}{3}-3)^2+(-2-1)^2}\)

\(r=\sqrt{(-\frac{2}{3})^2+(-3)^2}=\sqrt{\frac{4}{9}+9}=\sqrt{\frac{85}{9}}\)

\(r=\frac{\sqrt{85}}{3}\) 

 

Circular function

 

\(x^2+y^2=r^2\)

 

\(x^2+y^2=\frac{85}{9}\)

 

laugh  !

asinus  Apr 23, 2017
 #2
avatar+7318 
0

transformation (3,1),(0,-5),(-4,-2)

 

Parable of three points

 

\(y=ax^2+bx+c\)

 

A ) \(1=a\cdot 3^2+3b+c\\9a+3b+c=1\)

 

B)  \(-5=0a+0b+c\\c=-5\)

 

C)  \(-2=16a-4b+c\\16a-4b-5=-2\) 

 

A)  \(9a+3b-5=1\\a=\frac{6-3b}{9}\)

 

C)  \(16a-4b=3\\a=\frac{4b+3}{16}\)

 

A)&C)  \(\frac{6-3b}{9}=\frac{4b+3}{16}\\96-48b=36b+27\\84b=69\\b=\frac{69}{84}=\frac{3\cdot23}{2\cdot2\cdot21}\\b=0.821\)

 

A)&C)⇒A) \(a=\frac{6-3\cdot \frac{69}{84}}{9}=\frac{6}{9}-\frac{3\cdot69}{9\cdot84}\\a=0.393\)

 

\(\color{blue}{y=ax^2+bx+c\\y=0.393x^2+0.821x-5}\)

 

laugh  !

asinus  Apr 23, 2017

21 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.