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

AustinIce Sep 26, 2019

#1**+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'

ElectricPavlov Sep 26, 2019

#2**+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

CPhill Sep 26, 2019