+0  
 
0
298
1
avatar

Find the equation algebraically, of the parabola which passes through the points (10,-14) and (-2,10), and whose axis of symmetry is the equation x=2, using vertex form.

Guest May 5, 2014

Best Answer 

 #2
avatar+91435 
+8

Find the equation algebraically, of the parabola which passes through the points (10,-14) and (-2,10), and whose axis of symmetry is the equation x=2, using vertex form.

Interesting question

(10,-14),     (1)

(-2,10)         (2)

 Vertex(2, k)     (3)

$$(x-h)^2=4a(y-k)$$     where (h,k) is the vertex

$$(x-2)^2=4a(y-k)$$  

Using (10,-14) we have $$64=4a(-14-k)$$

Using (-2,10) we have    $$16=4a(10-k)$$

 $$\frac{64}{16}=\frac{4a(-14-k)}{4a(10-k)}\\\\
4=\frac{-14-k}{10-k}\\\\
4=\frac{-14-k}{10-k}\\\\
40-4k=-14-k\\\\
54=3k\\\\
k=18$$

---------------------

$$(x-2)^2=4a(y-18)$$

  $$(10,-14) 64=4a(-32)\rightarrow -2=4a \rightarrow a=-0.5\\
check
(-2,10) 16=4a(-8)\rightarrow a=-0.5\\$$

So the equation is 

$$(x-2)^2=-2(y-18)$$

And that is that.  Can I have a thumbs up now please. OR if you don't understand ask for clarification. 

Melody  May 6, 2014
Sort: 

1+0 Answers

 #2
avatar+91435 
+8
Best Answer

Find the equation algebraically, of the parabola which passes through the points (10,-14) and (-2,10), and whose axis of symmetry is the equation x=2, using vertex form.

Interesting question

(10,-14),     (1)

(-2,10)         (2)

 Vertex(2, k)     (3)

$$(x-h)^2=4a(y-k)$$     where (h,k) is the vertex

$$(x-2)^2=4a(y-k)$$  

Using (10,-14) we have $$64=4a(-14-k)$$

Using (-2,10) we have    $$16=4a(10-k)$$

 $$\frac{64}{16}=\frac{4a(-14-k)}{4a(10-k)}\\\\
4=\frac{-14-k}{10-k}\\\\
4=\frac{-14-k}{10-k}\\\\
40-4k=-14-k\\\\
54=3k\\\\
k=18$$

---------------------

$$(x-2)^2=4a(y-18)$$

  $$(10,-14) 64=4a(-32)\rightarrow -2=4a \rightarrow a=-0.5\\
check
(-2,10) 16=4a(-8)\rightarrow a=-0.5\\$$

So the equation is 

$$(x-2)^2=-2(y-18)$$

And that is that.  Can I have a thumbs up now please. OR if you don't understand ask for clarification. 

Melody  May 6, 2014

19 Online Users

avatar
avatar
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.  See details