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Find by algebraic means the point of intersection of two graphs with equations y=x^2-3x +7 and y= 5 - x^2.

 Sep 26, 2019
 #1
avatar+19832 
+2

Since it is a point of intersection.....the point will satisfy BOTH of the equations....and they are equal at this point...so set them equal to each other

 

x^2-3x+7  =  5 - x^2      and solve for 'x'     

                                            then use this value of 'x'    (there MAY be TWO values of 'x' !...and there may be NONE !!)  in one of the equations to compute 'y'  

 Sep 26, 2019
edited by ElectricPavlov  Sep 26, 2019
 #2
avatar+104962 
+1

x^2 - 3x + 7  = 5 - x^2         add x^2 to both sides......subtract 5 from both sides

 

2x^2 - 3x + 2  =  0        (1)

 

The dicriminant   is

 

(-3)^2 - 4(2)(2)  =

 

9  -  16  =

 

-7

 

Thus.....if the discriminant is negative, we have no real solutions to   (1)....so.....there are no intersection points  as shown by the graph here :

 

https://www.desmos.com/calculator/1gyqxrcryq

 

 

 

cool cool cool

 Sep 26, 2019
edited by CPhill  Sep 26, 2019

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