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Find all points, if any, where y - 4x = 12 intersects 2 - y = 2(x + 2)^2

 Feb 21, 2019
 #1
avatar+101870 
+2

Find all points, if any, where y - 4x = 12 intersects 2 - y = 2(x + 2)^2

 

Let's write the first as   y = 4x + 12

And the second as   y = 2 - 2(x + 2)^2

 

Set the y's equal and we have

 

2 - 2(x + 2)^2   =  4x + 12       simplify

 

2 - 2 [ x^2 + 4x + 4 ] = 4x + 12

 

2 - 2x^2 - 8x - 8 = 4x + 12

 

-2x^2 - 8x - 6   =  4x + 12       rearramge as

 

-2x^2 - 12x - 18 = 0        divide through by -2

 

x^2 + 6x + 9   =   0       factor

 

(x + 3)^2 = 0   take the square root

 

x + 3   =  0     subtract 3 from both sides

 

x = -3

 

And using y = 4x + 12

Then y =  4(-3) + 12  =  0

 

So....the solution is  ( - 3, 0 )

 

Here's the graph that confirms this :  https://www.desmos.com/calculator/6uplog6lqb

 

 

cool cool cool

 Feb 21, 2019
 #2
avatar+393 
+4

Thanks 😉😉😉

 Feb 21, 2019
 #3
avatar+101870 
0

No prob !!!

 

 

cool cool cool

CPhill  Feb 21, 2019

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